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We study a class of stochastic models of mass transport on discrete vertex set V. For these models, a one-parameter family of homogeneous product measures ⊗ i ∈ V ν θ is reversible. We prove that the set of mixtures of inhomogeneous product measures with equilibrium marginals, i.e., the set of measures of the form ∫ (⨂ i ∈ V ν θ i ) Ξ (∏ i ∈ V d θ i) is left invariant by the dynamics in the course of time, and the “mixing measure” Ξ evolves according to a Markov process which we then call “the hidden parameter model”. This generalizes results from De Masi et al. (Preprint , 2023) to a larger class of models and on more general graphs. The class of models includes discrete and continuous generalized KMP models, as well as discrete and continuous harmonic models. The results imply that in all these models, the non-equilibrium steady state of their reservoir driven version is a mixture of product measures where the mixing measure is in turn the stationary state of the corresponding “hidden parameter model”. For the boundary-driven harmonic models on the chain { 1 , … , N } with nearest neighbor edges, we recover that the stationary measure of the hidden parameter model is the joint distribution of the ordered Dirichlet distribution (cf. Carinci et al., Preprint , 2023), with a purely probabilistic proof based on a spatial Markov property of the hidden parameter model. [ABSTRACT FROM AUTHOR]

We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces. [ABSTRACT FROM AUTHOR]

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Following Beurling's theorem the natural compressions of the multiplication operator in the classical L 2 space are compressions to model spaces and to their orthogonal complements. Here, two possibly different model spaces are considered, hence asymmetric truncated Toeplitz and asymmetric dual truncated Toeplitz operators are investigated. The main purpose of the paper is to characterize operators which intertwine compressions of the unilateral shift. [ABSTRACT FROM AUTHOR]

Wilson (Proceedings of the twenty-eight annual acm symposium on the theory of computing, pp. 296-303, 1996) in the 1990s described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a powerful tool in analyzing structures on networks and along this line of thinking, in recent works (Avena and Gaudillière in A proof of the transfer-current theorem in absence of reversibility, in Stat. Probab. Lett. 142, 17-22 (2018); Avena and Gaudillière in J Theor Probab, 2017. 10.1007/s10959-017-0771-3; Avena et al. in Approximate and exact solutions of intertwining equations though random spanning forests, 2017. arXiv:1702.05992v1; Avena et al. in Intertwining wavelets or multiresolution analysis on graphs through random forests, 2017. arXiv:1707.04616, to appear in ACHA (2018)) we focused on applications of spanning rooted forests on finite graphs. The resulting main conclusions are reviewed in this paper by collecting related theorems, algorithms, heuristics and numerical experiments. A first foundational part on determinantal structures and efficient sampling procedures is followed by four main applications: (1) a random-walk-based notion of well-distributed points in a graph, (2) a framework to describe metastable-like dynamics in finite settings by means of Markov intertwining dualities, (3) coarse graining schemes for networks and associated processes, (4) wavelets-like pyramidal algorithms for graph signals. [ABSTRACT FROM AUTHOR]

We find all self-duality functions of the form D(ξ,η)=∏xd(ξx,ηx)for a class of interacting particle systems. We call these duality functions of simple factorized form. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion processes, as well as duality and self-duality functions for their continuous counterparts. The approach is based on, firstly, a general relation between factorized duality functions and stationary product measures and, secondly, an intertwining relation provided by generating functions. For the interacting particle systems, these self-duality and duality functions turn out to be generalizations of those previously obtained in Giardinà et al. (J Stat Phys 135:25-55, 2009) and, more recently, in Franceschini and Giardinà (Preprint, arXiv:1701.09115, 2016). Thus, we discover that only these two families of dualities cover all possible cases. Moreover, the same method discloses all simple factorized self-duality functions for interacting diffusion systems such as the Brownian energy process, where both the process and its dual are in continuous variables. [ABSTRACT FROM AUTHOR]

It is now generally accepted that human beings are naturally, possibly even essentially, intersubjective. This chapter offers a robust defence of an enhanced and extended intersubjectivity, criticising the paucity of individuating notions of agency and emphasising the community and reciprocity of our affective co-existence with other living organisms and things. I refer to this modified intersubjectivity, which most closely expresses the implicit intricacy of our pre-reflective neuro-muscular experiential entanglement, as 'enkinaesthesia'. The community and reciprocity of this entanglement is characterised as dialogical, and in this dialogue, as part of our anticipatory preparedness, we have a capacity for intentional transgression, feeling our way with our world but, more particularly, co-feeling our way with the mind and intentions of the other. Thus we are, not so much 'mind'-reading, as 'mind'-feeling, and it is through this enkinaesthetic 'mind'-feeling dialogue that values-realising activity originates and we uncover the deep roots of morality. [ABSTRACT FROM AUTHOR]

We obtain an intertwining relation between some Riemann-Liouville operators of order α ∈ (1, 2), connecting through a certain multiplicative identity in law the one-dimensional marginals of reflected completely asymmetric α-stable Lévy processes. An alternative approach based on recurrent extensions of positive self-similar Markov processes and exponential functionals of Lévy processes is also discussed. [ABSTRACT FROM AUTHOR]

A Banach space operator satisfies property ( R) if the set of its finite multiplicity isolated eigenvalues equals the set of its finite rank left poles. Property ( R) transfers from operators A and B to their tensor product A⊗ B. Asymptotic intertwining by the identity operator does not preserve property ( R). Additional hypotheses are required. [ABSTRACT FROM AUTHOR]

In his last work, The Visible and the Invisible, Merleau-Ponty explored the fact that we believe that perception occurs in our heads (“in the recesses of a body”) and, hence, assert that the perceptual world is “in” us, while also believing that we are “in” the world we perceive. In this article, I examine how this intertwining of self and world justifies the faith we have in perception. I shall do so by considering a number of examples. In each case, the object “in itself” will turn out to be neither within us nor outside of us, but rather at the intersection set by the intertwining. I will then turn to what this disclosure of this object reveals about human temporality and, indeed, about human being as a place (or “clearing”) that permits disclosure. [ABSTRACT FROM AUTHOR]