Search

In a previous paper (Kels in J Phys A 50(49):495202, 2017), the author has established an extension of the Z-invariance property for integrable edge-interaction models of statistical mechanics, that satisfy the star–triangle relation (STR) form of the Yang–Baxter equation (YBE). In the present paper, an analogous extended Z-invariance property is shown to also hold for integrable vector models and interaction-round-a-face (IRF) models of statistical mechanics respectively. As for the previous case of the STR, the Z-invariance property is shown through the use of local cubic-type deformations of a 2-dimensional surface associated to the models, which allow an extension of the models onto a subset of next nearest neighbour vertices of Z 3 , while leaving the partition functions invariant. These deformations are permitted as a consequence of the respective YBE's satisfied by the models. The quasi-classical limit is also considered, and it is shown that an analogous Z-invariance property holds for the variational formulation of classical discrete Laplace equations which arise in this limit. From this limit, new integrable 3D-consistent multi-component quad equations are proposed, which are constructed from a degeneration of the equations of motion for IRF Boltzmann weights. [ABSTRACT FROM AUTHOR]

In this paper, we continue our analysis of spatial versions of agent-based models for the dynamics of money that have been introduced in the statistical physics literature, focusing on two models with debts. Both models consist of systems of economical agents located on a finite connected graph representing a social network. Each agent is characterized by the number of coins she has, which can be negative in case she is in debt, and each monetary transaction consists in one coin moving from one agent to one of her neighbors. In the first model, that we name the model with individual debt limit, the agents are allowed to individually borrow up to a fixed number of coins. In the second model, that we name the model with collective debt limit, agents can borrow coins from a central bank as long as the bank is not empty, with reimbursements occurring each time an agent in debt receives a coin. Based on numerical simulations of the models on complete graphs, it was conjectured that, in the large population/temperature limits, the distribution of money converges to a shifted exponential distribution for the model with individual debt limit, and to an asymmetric Laplace distribution for the model with collective debt limit. In this paper, we prove exact formulas for the distribution of money that are valid for all possible social networks. Taking the large population/temperature limits in the formula found for the model with individual debt limit, we prove convergence to the shifted exponential distribution, thus establishing the first conjecture. Simplifying the formula found for the model with collective debt limit is more complicated, but using a computer to plot this formula shows an almost perfect fit with the Laplace distribution, which strongly supports the second conjecture. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the stationary harmonic measure in the upper half plane. By bounding this measure, we are able to define both the discrete and continuous time diffusion limited aggregation (DLA) in the upper half plane with absorbing boundary conditions. We prove that for the continuous model the growth rate is bounded from above by o (t 2 + ϵ) . Moreover we prove that all the moments are finite for the size of the aggregation. When time is discrete, we also prove a better upper bound of o (n 2 / 3 + ϵ) , on the maximum height of the aggregate at time n. An important tool developed in this paper, is an interface growth process, bounding any process growing according to the stationary harmonic measure. Together with [12] one obtains non zero growth rate for any such process. [ABSTRACT FROM AUTHOR]

We consider random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. In a companion paper, we have shown that if the random walk is pulled to the right by a positive bias λ > 0 , then its asymptotic linear speed v ¯ is continuous in the variable λ > 0 and differentiable for all sufficiently small λ > 0 . In the paper at hand, we complement this result by proving that v ¯ is differentiable at λ = 0 . Further, we show the Einstein relation for the model, i.e., that the derivative of the speed at λ = 0 equals the diffusivity of the unbiased walk. [ABSTRACT FROM AUTHOR]

We consider the open quantum random walks on the crystal lattices and investigate the central limit theorems for the walks. On the integer lattices the open quantum random walks satisfy the central limit theorems as was shown by Attal et al (Ann Henri Poincaré 16(1):15–43, 2015). In this paper we prove the central limit theorems for the open quantum random walks on the crystal lattices. We then provide with some examples for the Hexagonal lattices. We also develop the Fourier analysis on the crystal lattices. This leads to construct the so called dual processes for the open quantum random walks. It amounts to get Fourier transform of the probability densities, and it is very useful when we compute the characteristic functions of the walks. In this paper we construct the dual processes for the open quantum random walks on the crystal lattices providing with some examples. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the asymptotic behavior of the multi-dimensional elephant random walk (MERW). It is a non-Markovian random walk which has a complete memory of its entire history. A wide range of literature is available on the one-dimensional ERW. Surprisingly, no references are available on the MERW. The goal of this paper is to fill the gap by extending the results on the one-dimensional ERW to the MERW. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated logarithm and the quadratic strong law for the MERW. The asymptotic normality of the MERW, properly normalized, is also provided. In the superdiffusive regime, we prove the almost sure convergence as well as the mean square convergence of the MERW. All our analysis relies on asymptotic results for multi-dimensional martingales. [ABSTRACT FROM AUTHOR]

Just over 50 years ago, Pierre Hohenberg developed a rigorous proof of the non-existence of long-range order in a two-dimensional superfluid or superconductor at finite temperatures. The proof was immediately extended by Mermin and Wagner to the Heisenberg ferromagnet and antiferromagnet, and shortly thereafter, by Mermin to prove the absence of translational long-range order in a two-dimensional crystal, whether in quantum or classical mechanics. In this paper, we present an extension of the Hohenberg–Mermin–Wagner theorem to give a rigorous proof of the impossibility of long-range ferromagnetic order in an itinerant electron system without spin-orbit coupling or magnetic dipole interactions. We also comment on some situations where there are compelling arguments that long-range order is impossible but no rigorous proof has been given, as well as situations, such as a magnet with long range interactions, or orientational order in a two-dimensional crystal, where long-range order can occur that breaks a continuous symmetry. [ABSTRACT FROM AUTHOR]

This is the second part of a three part series abut delocalization for band matrices. In this paper, we consider a general class of N × N random band matrices H = (H ij) whose entries are centered random variables, independent up to a symmetry constraint. We assume that the variances E | H ij | 2 form a band matrix with typical band width 1 ≪ W ≪ N . We consider the generalized resolvent of H defined as G (Z) : = (H - Z) - 1 , where Z is a deterministic diagonal matrix such that Z ij = z 1 1 ⩽ i ⩽ W + z ~ 1 i > W δ ij , with two distinct spectral parameters z ∈ C + : = { z ∈ C : Im z > 0 } and z ~ ∈ C + ∪ R . In this paper, we prove a sharp bound for the local law of the generalized resolvent G for W ≫ N 3 / 4 . This bound is a key input for the proof of delocalization and bulk universality of random band matrices in Bourgade et al. (arXiv:1807.01559, 2018). Our proof depends on a fluctuations averaging bound on certain averages of polynomials in the resolvent entries, which will be proved in Yang and Yin (arXiv:1807.02447, 2018). [ABSTRACT FROM AUTHOR]

In this paper we revisit the problem of explaining phase transition by a study of a form of the Boltzmann equation, where inter-molecular attraction is included by means of a Vlasov term in the evolution equation for the one particle distribution function. We are able to show that for typical gas densities, a uniform state is unstable if the inter-molecular attraction is large enough. Our analysis relies strongly on the assumption, essential to the derivation of the Boltzmann equation, that ν≪1, where ν=d/l is the ratio of the molecular diameter to the mean inter-particle distance; in this case, for fluctuations on the scale of the molecular spacing, the collision term is small, and an explicit approximate solution is possible. We give reasons why we think the resulting approximation is valid, and in conclusion offer some possibilities for extension of the results to finite amplitude. [ABSTRACT FROM AUTHOR]

In this paper we study the phase transition of continuum Widom-Rowlinson measures in Rd with q types of particles and random radii. Each particle xi of type i is marked by a random radius ri distributed by a probability measure Qi on R+. The distributions Qi may be different for different i, this setting is called the non-symmetric case. The particles of same type do not interact with each other whereas a particle xi and xj with different type i≠j interact via an exclusion hardcore interaction forcing ri+rj to be smaller than |xi-xj|. In the symmetric integrable case (i.e. ∫rdQ1(dr)<+∞ and Qi=Q1 for every 1≤i≤q), we show that the Widom-Rowlinson measures exhibit a standard phase transition providing uniqueness, when the activity is small, and co-existence of q ordered phases, when the activity is large. In the non-integrable case (i.e. ∫rdQi(dr)=+∞, 1≤i≤q), we show another type of phase transition. We prove, when the activity is small, the existence of at least q+1 extremal phases and we conjecture that, when the activity is large, only the q ordered phases subsist. We prove a weak version of this conjecture in the symmetric case by showing that the Widom-Rowlinson measure with free boundary condition is a mixing of the q ordered phases if and only if the activity is large. [ABSTRACT FROM AUTHOR]

Synchronization of neurons forming a network with a hierarchical structure is essential for the brain to be able to function optimally. In this paper we study synchronization of phase oscillators on the most basic example of such a network, namely, the hierarchical lattice. Each site of the lattice carries an oscillator that is subject to noise. Pairs of oscillators interact with each other at a strength that depends on their hierarchical distance, modulated by a sequence of interaction parameters. We look at block averages of the oscillators on successive hierarchical scales, which we think of as block communities. In the limit as the number of oscillators per community tends to infinity, referred to as the hierarchical mean-field limit, we find a separation of time scales, i.e., each block community behaves like a single oscillator evolving on its own time scale. We argue that the evolution of the block communities is given by a renormalized mean-field noisy Kuramoto equation, with a synchronization level that depends on the hierarchical scale of the block community. We find three universality classes for the synchronization levels on successive hierarchical scales, characterized in terms of the sequence of interaction parameters. What makes our model specifically challenging is the non-linearity of the interaction between the oscillators. The main results of our paper therefore come in three parts: (I) a conjecture about the nature of the renormalisation transformation connecting successive hierarchical scales; (II) a truncation approximation that leads to a simplified renormalization transformation; (III) a rigorous analysis of the simplified renormalization transformation. We provide compelling arguments in support of (I) and (II), but a full verification remains an open problem. [ABSTRACT FROM AUTHOR]

This paper gives a short historical survey of basic events which had happend during the developmentb of chaos theory. [ABSTRACT FROM AUTHOR]

The Cauchy problem of the relativistic Enskog equation with near-vacuum data is considered in this paper. Under the same assumption as that in Jiang (J. Stat. Phys. 127:805–812, ) for the relativistic Enskog equation, we obtain the uniform L∞-stability of the solution. What’s more important, is that for two new types of the scattering cross section σ, we give the global existence and L1( x, v)-stability for mild solution when the initial data lies in the space L1( x, v). As a corollary, we have a BV-type estimate. It is worth mentioning that the stability results in this paper can be applied to the case in Jiang (J. Stat. Phys. 127:805–812, ). [ABSTRACT FROM AUTHOR]

In this paper, we study the free energy of the directed polymer on a cylinder of radius L with the inverse temperature β . Assuming the random environment is given by a Gaussian process that is white in time and smooth in space, with an arbitrary compactly supported spatial covariance function, we obtain precise scaling behaviors of the limiting free energy for high temperatures β ≪ 1 , followed by large L ≫ 1 , in all dimensions. Our approach is based on a perturbative expansion of the PDE hierarchy satisfied by the multipoint correlation function of the polymer endpoint distribution. For the random environment given by the 1 + 1 spacetime white noise, we derive an explicit expression of the limiting free energy. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of kinetic equations describing radiative transfer in gases which include also the interaction of the molecules of the gas with themselves. We discuss several scaling limits and introduce some Euler-like systems coupled with radiation as an aftermath of specific scaling limits. We consider scaling limits in which local thermodynamic equilibrium (LTE) holds, as well as situations in which this assumption fails (non-LTE). The structure of the equations describing the gas-radiation system is very different in the LTE and non-LTE cases. We prove the existence of stationary solutions with zero velocities to the resulting limit models in the LTE case. We also prove the non-existence of a stationary state with zero velocities in a non-LTE case. [ABSTRACT FROM AUTHOR]

The instability of mixing in the Kuramoto model of coupled phase oscillators is the key to understanding a range of spatiotemporal patterns, which feature prominently in collective dynamics of systems ranging from neuronal networks, to coupled lasers, to power grids. In this paper, we describe a codimension–2 bifurcation of mixing whose unfolding, in addition to the classical scenario of the onset of synchronization, also explains the formation of clusters and chimeras. We use a combination of linear stability analysis and Penrose diagrams to identify and analyze a variety of spatiotemporal patterns including stationary and traveling coherent clusters and twisted states, as well as their combinations with regions of incoherent behavior called chimera states. Penrose diagrams are used to locate the bifurcation of mixing and to determine its type. The linear stability analysis, on the other hand, yields the velocity distribution of the pattern emerging from the bifurcation. Furthermore, we show that network topology can endow chimera states with nontrivial spatial organization. In particular, we present twisted chimera states, whose coherent regions are organized as stationary or traveling twisted states. The analytical results are illustrated with numerical bifurcation diagrams computed for the Kuramoto model with uni-, bi-, and trimodal frequency distributions and all-to-all and nonlocal nearest-neighbor connectivity. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate the collapsed phase of the interacting partially-directed self-avoiding walk (IPDSAW) that was introduced in Zwanzig and Lauritzen (J Chem Phys 48(8):3351, 1968) under a semi-continuous form and later in Binder et al. (J Phys A 23(18):L975–L979, 1990) under the discrete form that we address here. We provide sharp asymptotics of the partition function inside the collapsed phase, proving rigorously a conjecture formulated in Guttmann (J Phys A 48(4):045209, 2015) and Owczarek et al. (Phys Rev Lett 70:951–953, 1993). As a by-product of our result, we obtain that, inside the collapsed phase, a typical IPDSAW trajectory is made of a unique macroscopic bead, consisting of a concatenation of long vertical stretches of alternating signs, outside which only finitely many monomers are lying. [ABSTRACT FROM AUTHOR]

Through an exact analysis, we show the existence of Mpemba effect in an anisotropically driven inelastic Maxwell gas, a simplified model for granular gases, in two dimensions. Mpemba effect refers to the couterintuitive phenomenon of a hotter system relaxing to the steady state faster than a cooler system, when both are quenched to the same lower temperature. The Mpemba effect has been illustrated in earlier studies on isotropically driven granular gases, but its existence requires non-stationary initial states, limiting experimental realisation. In this paper, we demonstrate the existence of the Mpemba effect in anisotropically driven Maxwell gases even when the initial states are non-equilibrium steady states. The precise conditions for the Mpemba effect, its inverse, and the stronger version, where the hotter system cools exponentially faster are derived. [ABSTRACT FROM AUTHOR]

This paper considers three classes of interacting particle systems on Z : independent random walks, the exclusion process, and the inclusion process. Particles are allowed to switch their jump rate (the rate identifies the type of particle) between 1 (fast particles) and ϵ ∈ [ 0 , 1 ] (slow particles). The switch between the two jump rates happens at rate γ ∈ (0 , ∞) . In the exclusion process, the interaction is such that each site can be occupied by at most one particle of each type. In the inclusion process, the interaction takes places between particles of the same type at different sites and between particles of different type at the same site. We derive the macroscopic limit equations for the three systems, obtained after scaling space by N - 1 , time by N 2 , the switching rate by N - 2 , and letting N → ∞ . The limit equations for the macroscopic densities associated to the fast and slow particles is the well-studied double diffusivity model. This system of reaction-diffusion equations was introduced to model polycrystal diffusion and dislocation pipe diffusion, with the goal to overcome the limitations imposed by Fick’s law. In order to investigate the microscopic out-of-equilibrium properties, we analyse the system on [ N ] = { 1 , … , N } , adding boundary reservoirs at sites 1 and N of fast and slow particles, respectively. Inside [N] particles move as before, but now particles are injected and absorbed at sites 1 and N with prescribed rates that depend on the particle type. We compute the steady-state density profile and the steady-state current. It turns out that uphill diffusion is possible, i.e., the total flow can be in the direction of increasing total density. This phenomenon, which cannot occur in a single-type particle system, is a violation of Fick’s law made possible by the switching between types. We rescale the microscopic steady-state density profile and steady-state current and obtain the steady-state solution of a boundary-value problem for the double diffusivity model. [ABSTRACT FROM AUTHOR]

In this paper, we study a model of directed polymers in random environment, where the environment is restricted to a time-space tube whose spatial width grows polynomially with time. It can be viewed as an interpolation between the disordered pinning model and the classic directed polymer model. We prove weak coupling limits for the directed polymer partition functions in such tube environments in all dimensions, as the inverse temperature vanishes at a suitable rate. As the tube width varies, transitions between regimes of disorder irrelevance, marginal relevance and disorder relevance are observed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the initial boundary value problem of the Vlasov–Fokker–Planck equation coupled with either the incompressible or compressible Navier–Stokes equations in a bounded domain. The global existence of unique strong solution and its exponential convergence rate to the equilibrium state are proved under the Maxwell boundary condition for the incompressible case and specular reflection boundary condition for the compressible case, respectively. For the compressible model, to overcome the lack of regularity due to the coupling with the kinetic equation in a bounded domain, an essential L 10 3 estimate is analyzed so that the a priori estimate can be closed by applying the S L p theory developed by Guo et al. for kinetic models, [Arch Ration Mech Anal 236(3): 1389–1454 (2020)]. [ABSTRACT FROM AUTHOR]

In this paper we analyze metastability and nucleation in the context of the Kawasaki dynamics for the two-dimensional Ising lattice gas at very low temperature. Let Λ ⊂ Z 2 be a finite box. Particles perform simple exclusion on Λ , but when they occupy neighboring sites they feel a binding energy - U 1 < 0 in the horizontal direction and - U 2 < 0 in the vertical one. Thus the Kawasaki dynamics is conservative inside the volume Λ . Along each bond touching the boundary of Λ from the outside to the inside, particles are created with rate ρ = e - Δ β , while along each bond from the inside to the outside, particles are annihilated with rate 1, where β > 0 is the inverse temperature and Δ > 0 is an activity parameter. Thus, the boundary of Λ plays the role of an infinite gas reservoir with density ρ . We consider the parameter regime U 1 > 2 U 2 also known as the strongly anisotropic regime. We take Δ ∈ (U 1 , U 1 + U 2) , so that the empty (respectively full) configuration is a metastable (respectively stable) configuration. We consider the asymptotic regime corresponding to finite volume in the limit as β → ∞ . We investigate how the transition from empty to full takes place with particular attention to the critical configurations that asymptotically have to be crossed with probability 1. The derivation of some geometrical properties of the saddles allows us to identify the full geometry of the minimal gates and their boundaries for the nucleation in the strongly anisotropic case. We observe very different behaviors for this case with respect to the isotropic ( U 1 = U 2 ) and weakly anisotropic ( U 1 < 2 U 2 ) ones. Moreover, we derive mixing time, spectral gap and sharp estimates for the asymptotic transition time for the strongly anisotropic case. [ABSTRACT FROM AUTHOR]

In this paper, we will establish two kinds of averaging principles for stochastic 2D Navier–Stokes equations, i.e. Bogoliubov averaging principle and Stratonovich–Khasminskii averaging principle. These averaging principles are powerful tools for studying asymptotic behavior of stochastic 2D Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

It is well known that, if the initial conditions have sufficiently high energy density, the dynamics of the classical Discrete Non-Linear Schrödinger Equation (DNLSE) on a lattice shows a form of breaking of ergodicity, with a finite fraction of the total charge accumulating on a few sites and residing there for times that diverge quickly in the thermodynamic limit. In this paper we show that this kind of localization can be attributed to some geometric properties of the microcanonical potential energy surface, and that it can be associated to a phase transition in the lowest eigenvalue of the Laplacian on said surface. We also show that the approximation of considering the phase space motion on the potential energy surface only, with effective decoupling of the potential and kinetic partition functions, is justified in the large connectivity limit, or fully connected model. In this model we further observe a synchronization transition, with a synchronized phase at low temperatures. [ABSTRACT FROM AUTHOR]

Over the past decades, many kinds of generalized statistics are proposed through two approaches: (1) generalizing the permutation symmetry of the wave function and (2) generalizing the maximum occupation of the quantum state. Nevertheless, the connection between these two approaches is obscure. In this paper, we suggest a unified framework to describe various kinds of generalized statistics by using the representation theory of the permutation group and the unitary group. With this approach, we reveal the connection between the permutation phase and the maximum occupation number, through constructing a method to obtain the permutation phase and the maximum occupation number from the canonical partition function. We show that only bosonic and fermionic particles are completely indistinguishable under permutations. Particles obeying generalized statistics are not completely indistinguishable and thus are not quantum particles. Besides, we also give the following results: (1) providing a general formula of canonical partition functions of ideal N-particle gases who obey various kinds of generalized statistics, (2) revealing that the maximum occupation number is not sufficient to distinguish different kinds of generalized statistics, (3) specifying the permutation phases of wave functions for generalized statistics, and (4) proposing three new kinds of generalized statistics which seem to be the missing pieces in the puzzle. [ABSTRACT FROM AUTHOR]

In this paper, we derive second order hydrodynamic traffic models from kinetic-controlled equations for driver-assist vehicles. At the vehicle level we take into account two main control strategies synthesising the action of adaptive cruise controls and cooperative adaptive cruise controls. The resulting macroscopic dynamics fulfil the anisotropy condition introduced in the celebrated Aw–Rascle–Zhang model. Unlike other models based on heuristic arguments, our approach unveils the main physical aspects behind frequently used hydrodynamic traffic models and justifies the structure of the resulting macroscopic equations incorporating driver-assist vehicles. Numerical insights show that the presence of driver-assist vehicles produces an aggregate homogenisation of the mean flow speed, which may also be steered towards a suitable desired speed in such a way that optimal flows and traffic stabilisation are reached. [ABSTRACT FROM AUTHOR]

In earlier work we showed that in the bulk, the correlation of gaps in dimer systems on the hexagonal lattice is governed, in the fine mesh limit, by Coulomb’s law for 2D electrostatics. We also proved that the scaling limit of the discrete field F of average tile orientations is, up to a multiplicative constant, the electric field produced by a 2D system of charges corresponding to the gaps. In this paper we show that in the bulk, the relative change T α , β in correlation caused by displacing a hole by a fixed vector (α , β) is, in the fine mesh limit, the projection on (α , β) of a new field T , which is also equal up to a multiplicative constant to the electric field of the corresponding system of charges. We also discuss the differences between the fields T and F and present conjectures for their fine mesh limits in the more general case of a dimer system with boundary. The new field T can be viewed as capturing the instantaneous pull on each gap in the surrounding fluctuating sea of dimers. From the point of view of the parallel to physics, the electrostatic force emerges then as an entropic force. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the relativistic Landau and Boltzmann equations in the whole space R 3 under the closed to equilibrium setting. We recognize the finite speed of propagation of the solution which was constructed by Yang and Yu (J Differ Equ 248:1518–1560, 2010). Moreover, the propagation speed can be as close as we want to the maximum speed of the transport part of the kinetic equation. [ABSTRACT FROM AUTHOR]

This paper is devoted to the asymptotic analysis of the reinforced elephant random walk (RERW) using a martingale approach. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated logarithm and the quadratic strong law for the RERW. The distributional convergences of the RERW to some Gaussian processes are also provided. In the superdiffusive regime, we prove the distributional convergence as well as the mean square convergence of the RERW. All our analysis relies on asymptotic results for multi-dimensional martingales with matrix normalization. [ABSTRACT FROM AUTHOR]

In a recent paper, Nagle criticized the new definition of entropy that I had proposed in an earlier work. In the examples for which Nagle claims my definition fails, he took a formula that I had derived for one set of experiments and used it to represent my definition for other experiments. However, the formulas obtained from my definition depend on the specific experimental observables. If my definition is correctly applied to Nagle’s experiments, no contradictions remain. [ABSTRACT FROM AUTHOR]

Thirty years after the Liu–Fisher paper on the bicritical and tetracritical points in quantum lattice gases, these multicritical points continue to appear in a variety of new physical contexts. This paper reviews some recent multicritical phase diagrams, which involve, e.g., high-Tc superconductivity and various magnetic phases which may (or may not) coexist with it. One recent example concerns the SO(5) theory, which combines the 3-component antiferromagnetic and the 2-component superconducting order parameters. There, the competition between the isotropic, biconical and decoupled fixed points yields bicritical or tetracritical points. Recalling old results on the subject, it is shown that the decoupled fixed point is stable, implying a tetracritical point, contrary to recent claims, which are critically discussed. Other examples, concerning, e.g., the superconducting versus charge and spin density wave phases are also discussed briefly. In all cases, extensions of old results can be used to correct new claims. [ABSTRACT FROM AUTHOR]

We present the analysis of experimental data that supports the recently presented hypothesis that the relationship between local areal density and local thickness in planar stochastic fiber networks may be described by the bivariate normal distribution. Measurements of the local averages of areal density and thickness have been made on experimental fiber networks with differing degrees of structural uniformity. The experimentally determined variance of local density at the 1 mm scale is in excellent agreement with that calculated from the theory. Also, the use of the bivariate normal distribution to describe the relationship between local areal density and local thickness measured in complete sampling schemes is appropriate for both near-random and clumped networks. [ABSTRACT FROM AUTHOR]

The Digital Annealer is a CMOS hardware designed by Fujitsu Laboratories for high-speed solving of Quadratic Unconstrained Binary Optimization (QUBO) problems that could be difficult to solve by means of existing general-purpose computers. In this paper, we present a mathematical description of the first-generation Digital Annealer's Algorithm from the Markov chain theory perspective, establish a relationship between its stationary distribution with the Gibbs-Boltzmann distribution, and provide a necessary and sufficient condition on its cooling schedule that ensures asymptotic convergence to the ground states. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain polynomial decay of correlations of a Lorenz-like flow where the hyperbolic saddle at the origin is replaced by a neutral saddle. To do that, we take the construction of the geometrical Lorenz flow and proceed by changing the nature of the saddle fixed point at the origin by a neutral fixed point. This modification is accomplished by changing the linearised vector field in a neighbourhood of the origin for a neutral vector field. This change in the nature of the fixed point will produce polynomial tails for the Dulac times, and combined with methods of Araújo and Melbourne (used to prove exponential mixing for the classical Lorenz flow) this will ultimately lead to polynomial upper bounds of the decay of correlations for the modified flow. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Borel measurable map of a compact metric space which admits an inducing scheme. Under the finite weighted complexity condition, we establish a thermodynamic formalism for a parameter family of potentials φ + t ψ in an interval containing t = 0 . Furthermore, if there is a generating partition compatible to the inducing scheme, we show that all ergodic invariant measures with sufficiently large pressure are liftable. Baladi and Demers (J Am Math Soc 33(2):381–449, 2020; J Mod Dyn 18:415–493, 2022) established general thermodynamic formalism for the Sinai dispersing billiards. As an application, our results provide an alternative proof for the existence, uniqueness and statistical properties of the equilibrium measures for the Sinai dispersing billiards with respect to the family of geometric potentials. [ABSTRACT FROM AUTHOR]

In this paper we show the existence of the minimal solution to the multidimensional Lambert–Euler inversion, a multidimensional generalization of [ - e - 1 , 0) branch of Lambert W function W 0 (x) . Specifically, for a given nonnegative irreducible symmetric matrix V ∈ R k × k and a vector u ∈ (0 , ∞) k , we show that, if the system of equations y j exp { - e j T V y } = u j ∀ j = 1 , ... , k , has at least one solution, it must have a minimal solution y ∗ , where the minimum is achieved in all coordinates y j simultaneously. Moreover, such y ∗ is the unique solution satisfying ρ V D [ y j ∗ ] ≤ 1 , where D [ y j ∗ ] = diag (y j ∗) is the diagonal matrix with entries y j ∗ and ρ denotes the spectral radius. Our main application is in the analysis of the vector-multiplicative coalescent process. It is a coalescent process with k types of particles and k-dimensional vector-valued cluster weights representing the composition of a cluster by particle types. The clusters merge according to the vector-multiplicative kernel K (x , y) = x T V y . First, we derive some new combinatorial results, and use them to solve the corresponding modified Smoluchowski equations obtained as a hydrodynamic limit of vector-multiplicative coalescent. Then, we use multidimensional Lambert–Euler inversion to establish gelation and find a closed form expression for the gelation time. We also find the asymptotic length of the minimal spanning tree for a broad range of graphs equipped with random edge lengths. [ABSTRACT FROM AUTHOR]

Entropy is widely applied to graph theory and complex networks as a powerful tool for measuring uncertainty in a complex system. Due to the fact that traditional probability distribution entropy cannot effectively characterize the global topology information of complex networks, some entropy measures constructed by the adjacency matrix A come into being, such as information-theoretic entropy EE and communicability sequence entropy. Despite substantial efforts to explore the properties of these measures, there remain some imperfections. For instance, the adjacency matrix only reflects the dependence between direct neighbors. Therefore, in this paper, we propose the r -power adjacency matrix entropy ( AME r ) to measure the indirect relationship between nodes in a network. And then, we compare the abilities of AME r , EE, and CSE in capturing the network global topology changes. Furthermore, we establish the Jenson–Shannon divergence based on AME r to quantify the structural dissimilarities of the networks. Finally, we apply the proposed methods to analyze the urban economic connection networks. The results demonstrate the availability of the proposed measures in identifying network topology changes and quantifying network structure differences. [ABSTRACT FROM AUTHOR]

In this paper, we prove the global existence and moment propagation of weak solutions for the repulsive plasma-charge model with a time-varying magnetic field. Multi-point charges are allowed according to an improved mechanism to compensate the asymmetry caused by the point charges, which brings us back to the standard Lions-Perthame’s argument. To deal with two type singularities induced by the point charges and the magnetic field, we combine the ideas from Desvillettes et al. (Ann Inst H Poincaré Anal Non Linéaire 32(2):373–400, 2015) and Rege (SIAM J Math Anal 53(2):2452–2475, 2021). The density of the plasma is allowed to be constant around the point charges, by applying the moment lemma established in Perthame (Math Methods Appl Sci 13(5):41–452, 1990) and careful compactness argument. The result answers two questions raised in Desvillettes et al. (Ann Inst H Poincaré Anal Non Linéaire 32(2):373–400, 2015). [ABSTRACT FROM AUTHOR]

In this paper we study the properties of the centered (norm of the) gradient squared of the discrete Gaussian free field in U ε = U / ε ∩ Z d , U ⊂ R d and d ≥ 2 . The covariance structure of the field is a function of the transfer current matrix and this relates the model to a class of systems (e.g. height-one field of the Abelian sandpile model or pattern fields in dimer models) that have a Gaussian limit due to the rapid decay of the transfer current. Indeed, we prove that the properly rescaled field converges to white noise in an appropriate local Besov-Hölder space. Moreover, under a different rescaling, we determine the k-point correlation function and joint cumulants on U ε and in the continuum limit as ε → 0 . This result is related to the analogue limit for the height-one field of the Abelian sandpile (Dürre in Stoch Process Appl 119(9):2725–2743, 2009), with the same conformally covariant property in d = 2 . [ABSTRACT FROM AUTHOR]

In this paper, we consider a generalization of the elephant random walk model. Compared to the usual elephant random walk, an interesting feature of this model is that the step sizes form a sequence of positive independent and identically distributed random variables instead of a fixed constant. For this model, we establish the law of the iterated logarithm, the central limit theorem, and we obtain rates of convergence in the central limit theorem with respect to the Kolmogorov, Zolotarev and Wasserstein distances. We emphasize that, even in case of the usual elephant random walk, our results concerning the rates of convergence in the central limit theorem are new. [ABSTRACT FROM AUTHOR]

This paper considers the stability of solutions around a global Maxwellian to the fully non-linear Fokker–Planck equation in the whole space. This model preserves mass, momentum and energy at the same time, and its dissipation is much weaker than that in the simplified model considered in Liao et al. (J Stat Phys 173:222–241, 2018). To overcome the new difficulties, the macro–micro decomposition of the solution around the local Maxwellian and energy estimates introduced in Liu et al. (Physica D 188:178–192, 2004) and Yang and Zhao (J Math Phys 47:053301, 2006) for Boltzmann equation is used. That is, we reformulate the model into a fluid-type system coupled with an equation of the microscopic part. The a priori estimates of the solution could be obtained by the standard energy method. Especially, by careful computation, the viscosity and heat diffusion terms in the fluid-type system are derived from the microscopic part, which give the dissipative mechanism to the system. [ABSTRACT FROM AUTHOR]

In this paper, we consider a pruned Galton–Watson tree conditioned to have k particles in generation n, i.e. we take a Galton–Watson tree satisfying Z n = k , and delete all branches that die before generation n. We show that with k fixed and n → ∞ , the first n generations of this tree can be described by an explicit probability measure P k st . As an application, we study a branching random walk (V u) u ∈ T indexed by such a pruned Galton–Watson tree T, and give the asymptotic tail behavior of the span and gap statistics of its k particles in generation n, (V u) | u | = n . This is the discrete version of Ramola et al. (Chaos Solitons Fractals 74:79–88, 2015), generalized to arbitrary offspring and displacement distributions with moment constraints. [ABSTRACT FROM AUTHOR]

In this paper, we study various notions of local pressure of subsets and measures with respect to a fixed open cover, which are defined by Carathéordory–Pesin construction. We show that all local pressures of an ergodic measure equal the local metric entropy defined by Romagnoli (Ergod Theory Dyn Syst, 23(05):1601–1610, 2003) plus the integral of potential up to a variation of potential with respect to the open cover. In particular, this answers positively a question by Downarowicz (Entropy in dynamical systems, New Mathematical Monographs, vol 18, Cambridge University Press, xii+391, 2011) on variant entropy. As analogs of local variational principles, we also establish variational inequalities for local pressure of subsets. [ABSTRACT FROM AUTHOR]

Flat-band systems are ideal model systems to study strong correlations. In a large class of one or two dimensional bosonic systems with a lowest flat-band it has been shown that at a critical density the ground states are Wigner crystals. Under very special conditions it has been shown that pair formation occurs if one adds another particle to the system. The present paper extends this result to a much larger class of lattices and to a much broader region in the parameter space. Further, a lower bound for the energy gap between these pair states and the rest of the spectrum is established. The pair states are dominated by a subspace spanned by states containing a compactly localised pair. Overall, this strongly suggests localised pair formation in the ground states of the broad class of flat-band systems and rigorously proves it for some of the graphs in it, including the inhomogeneous chequerboard chain as well as two novel examples of regular two dimensional graphs. Physically, this means that the Wigner crystal remains intact if one adds a particle to it. [ABSTRACT FROM AUTHOR]

Beta ensembles on the real line with three classical weights (Gaussian, Laguerre and Jacobi) are now realized as the eigenvalues of certain tridiagonal random matrices. The paper deals with beta Jacobi ensembles, the type with the Jacobi weight. Making use of the random matrix model, we show that in the regime where β N → c o n s t ∈ [ 0 , ∞) , with N the system size, the empirical distribution of the eigenvalues converges weakly to a limiting measure which belongs to a new class of probability measures of associated Jacobi polynomials. This is analogous to the existing results for the other two classical weights. We also study the limiting behavior of the empirical measure process of beta Jacobi processes in the same regime and obtain a dynamical version of the above. [ABSTRACT FROM AUTHOR]