Search

The CYGNO experiment aims to build a large ($\mathcal{O}(10)$ m$^3$) directional detector for rare event searches, such as nuclear recoils (NRs) induced by dark matter (DM), such as weakly interactive massive particles (WIMPs). The detector concept comprises a time projection chamber (TPC), filled with a He:CF$_4$ 60/40 scintillating gas mixture at room temperature and atmospheric pressure, equipped with an amplification stage made of a stack of three gas electron multipliers (GEMs) which are coupled to an optical readout. The latter consists in scientific CMOS (sCMOS) cameras and photomultipliers tubes (PMTs). The maximisation of the light yield of the amplification stage plays a major role in the determination of the energy threshold of the experiment. In this paper, we simulate the effect of the addition of a strong electric field below the last GEM plane on the GEM field structure and we experimentally test it by means of a 10$\times$10 cm$^2$ readout area prototype. The experimental measurements analyse stacks of different GEMs and helium concentrations in the gas mixture combined with this extra electric field, studying their performances in terms of light yield, energy resolution and intrinsic diffusion. It is found that the use of this additional electric field permits large light yield increases without degrading intrinsic characteristics of the amplification stage with respect to the regular use of GEMs.

The CYGNO collaboration is developing next generation directional Dark Matter (DM) detection experiments, using gaseous Time Projection Chambers (TPCs), as a robust method for identifying Weakly Interacting Massive Particles (WIMPs) below the Neutrino Fog. SF6 is potentially ideal for this since it provides a high fluorine content, enhancing sensitivity to spin-dependent interactions and, as a Negative Ion Drift (NID) gas, reduces charge diffusion leading to improved positional resolution. CF4, although not a NID gas, has also been identified as a favourable gas target as it provides a scintillation signal which can be used for a complimentary light/charge readout approach. These gases can operate at low pressures to elongate Nuclear Recoil (NR) tracks and facilitate directional measurements. In principle, He could be added to low pressure SF6/CF4 without significant detriment to the length of 16S, 12C, and 19F recoils. This would improve the target mass, sensitivity to lower WIMP masses, and offer the possibility of atmospheric operation; potentially reducing the cost of a containment vessel. In this article, we present gas gain and energy resolution measurements, taken with a Multi-Mesh Thick Gaseous Electron Multiplier (MMThGEM), in low pressure SF6 and CF4:SF6 mixtures following the addition of He. We find that the CF4:SF6:He mixtures tested were able to produce gas gains on the order of 10^4 up to a total pressure of 100 Torr. These results demonstrate an order of magnitude improvement in charge amplification in NID gas mixtures with a He component., Comment: Corresponding Author: A.G. McLean

Low pressure gaseous Time Projection Chambers (TPCs) are a viable technology for directional Dark Matter (DM) searches and have the potential for exploring the parameter space below the neutrino fog. Gases like CF4 are advantageous because they contain flourine which is predicted to have heightened elastic scattering rates with a possible Weakly Interacting Massive Particle (WIMP) DM candidate. The low pressure of CF4 must be maintained, ideally lower than 100 Torr, in order to elongate potential Nuclear Recoil (NR) tracks which allows for improved directional sensitivity and NR/Electron Recoil (ER) discrimination. Recent evidence suggests that He can be added to heavier gases, like CF4, without significantly affecting the length of 12C and 19F recoils due to its lower mass. Such addition of He has the advantage of improving sensitivity to lower mass WIMPs. Simulations can not reliably predict operational stability in these low pressure gas mixtures and thus must be demonstrated experimentally. In this paper we investigate how the addition of He to low pressure CF4 affects the gas gain and energy resolution achieved with a single Thick Gaseous Electron Multiplier (ThGEM).

In the field of directional dark matter experiments, SF6 has emerged as an ideal target gas. A critical challenge with this gas, and with other proposed gases, is the effective removal of contaminant gases. This includes radon which produce unwanted background events, but also common pollutants such as water, oxygen, and nitrogen, which can capture ionisation electrons, resulting in loss of detector gas gain over time. We present here a novel molecular sieve (MS) based gas recycling system for the simultaneous removal of both radon and common pollutants from SF6. The apparatus has the additional benefit of minimising gas required in experiments and utilises a Vacuum Swing Adsorption (VSA) technique for continuous, long-term operation. The gas system's capabilities were tested with a 100 L low-pressure SF6 Time Projection Chamber (TPC) detector. For the first time, we present a newly developed low-radioactive MS type 5A. This material was found to emanate radon at 98% less per radon captured compared to commercial counterparts, the lowest known MS emanation at the time of writing. Consequently, the radon activity in the TPC detector was reduced, with an upper limit of less than 7.2 mBq at a 95% confidence level (C.L.). Incorporation of MS types 3A and 4A to absorb common pollutants was found successfully to mitigate against gain deterioration while recycling the target gas.

The Negative Ion Drift (NID) gas SF$_6$ has favourable properties for track reconstruction in directional Dark Matter (DM) searches utilising low pressure gaseous Time Projection Chambers (TPCs). However, the electronegative nature of the gas means that it is more difficult to achieve significant gas gains with regular Thick Gaseous Electron Multipliers (ThGEMs). Typically, the maximum attainable gas gain in SF$_6$ and other Negative Ion (NI) gas mixtures, previously achieved with an $^{55}$Fe X-ray source or electron beam, is on the order of $10^3$; whereas electron drift gases like CF$_4$ and similar mixtures are readily capable of reaching gas gains on the order of $10^4$ or greater. In this paper, a novel two stage Multi-Mesh ThGEM (MMThGEM) structure is presented. The MMThGEM was used to amplify charge liberated by an $^{55}$Fe X-ray source in 40 Torr of SF$_6$. By expanding on previously demonstrated results, the device was pushed to its sparking limit and stable gas gains up to $\sim$50000 were observed. The device was further optimised by varying the field strengths of both the collection and transfer regions in isolation. Following this optimisation procedure, the device was able to produce a maximum stable gas gain of $\sim$90000. These results demonstrate an order of magnitude improvement in gain with the NID gas over previously reported values and ultimately benefits the sensitivity of a NITPC to low energy recoils in the context of a directional DM search.

We consider a model of directed polymers on regular trees with complex-valued random weights introduced by Cook and Derrida [CD90] and studied mathematically by Derrida, Evans and Speer [DES93]. In addition to the usual weak-disorder and strong-disorder regimes, the phase diagram of the model contains a third region due to the effects of the random phases that cannot be observed in the model with positive weights. In this work, we extend the results of [DES93] in two directions. First, we remove the hypothesis on the independence of the random radii and random phases of the environment from most of the phase diagram, and second, under mild assumptions on the law of the environment, we strengthen the convergence of the free energy (shown to hold in probability in [DES93]) to an almost sure convergence. Along the way, many of the arguments of [DES93] are simplified.

The CYGNO project aims at the development of a high precision optical readout gaseous Tima Projection Chamber (TPC) for directional dark matter (DM) searches, to be hosted at Laboratori Nazionali del Gran Sasso (LNGS). CYGNO employs a He:CF$_4$ gas mixture at atmospheric pressure with a Gas Electron Multiplier (GEM) based amplification structure coupled to an optical readout comprised of sCMOS cameras and photomultiplier tubes (PMTs). This experimental setup allows to achieve 3D tracking and background rejection down to O(1) keV energy, to boost sensitivity to low WIMP masses. The characteristics of the optical readout approach in terms of the light yield will be illustrated along with the particle identification properties. The project timeline foresees, in the next 2-3 years, the realisation and installation of a 0.4 m$^3$ TPC in the underground laboratories at LNGS to act as a demonstrator. Finally, the studies of the expected DM sensitivities of the CYGNO demonstrator will be presented.

We consider one-dimensional discrete Dirac models in vanishing random environments. In a previous work [6], we showed that these models exhibit a rich phase diagram in terms of their spectrum as a function of the rate of decay of the random potential. This article is devoted to their spectral statistics. We show that the rescaled spectrum converges to the clock process for fast decay and to the Schr\"odinger/Sine processes from random matrix theory for critical decay. This way, we recover all the regimes previously identified for the Anderson model in a similar context [25]. Poisson statistics, which should appear in the model with slow decay, are left as an open problem. The core of the proof consists in a suitable scaling limit for the Pr\"ufer phase and monotonicity arguments, yielding an alternative to the approach of [25]. For one of the models, we also obtain the scaling limit of the Pr\"ufer radii and discuss the consequences for the limiting shape of the eigenfunctions.

We show that using the process of one-axis-twist squeezing in an echo configuration, it is possible to control the orientation of the macroscopic magnetic moment of a large number of atoms by manipulating the quantum state of a single atom that is physically isolated from the ensemble. With this control technique, it is also possible to entangle an ensemble with a single atom deterministically, which mimics the thought experiment known as the Schr\"odinger cat. In addition, this technique would make it possible to generate a mesoscopic Schr\"odinger cat state for a large number of atoms far more rapidly that the conventional process for generating such a state, with an orientation that is independent of the parity of the number of atoms. Apart from the echo configuration, we have also investigated the behavior of one-axis-twist squeezing for some special values of the squeezing parameter. We find that the squeezing propagator can be expressed as the sum of n rotation operators if the product of n and the squeezing parameter equals pi, where n is a non-zero integer. A direct consequence of this property of one-axis-twist squeezing is that there is a hidden order in a squeezed state generated under this condition even if its Husimi quasi-probability distribution looks irregular.

We theoretically investigate the feasibility of applying spin squeezing to a light pulse atom interferometer in the presence of large momentum transfer using off-resonant Raman transitions, in order to enhance the sensitivity of accelerometry close to the Heisenberg limit. We also show how to implement this scheme in a dual-species atom interferometer for precision test of the equivalence principle by measuring the Eotvos parameter, and identify the spin squeezing protocol that is best suited for such an experiment. For a space borne platform in low earth orbit, such a scheme may eventually enable the measurement of the Eotvos parameter with a sensitivity of the order of 10^(-20).

We present a generalized echo squeezing protocol (GESP) as a generalization of the Schr\"odinger cat state protocol (SCSP) with the value of the squeezing parameter being an arbitrary number rather than pi/2. We show analytically that over a broad range of the squeezing parameter the sensitivity reaches the Heisenberg limit (HL) within a factor of root-2. For a large number of particles, N, this plateau interval is almost the whole range from zero to pi/2, and the sensitivity is independent of the parity of N. Therefore, it is possible to operate a sensor over a wide interval of the squeezing parameter without changing the sensitivity. This is to be contrasted with the conventional echo squeezing protocol (CESP) which only works for a very small interval. In contrast to the CESP, the sensitivity of the GESP is close to the quantum Cram\'er-Rao bound over the whole range of the squeezing parameter. The enhancement in sensitivity for the GESP is due to a combination of two parameters: the phase magnification factor (PMF) and the noise amplification factor (NAF). As the value of the squeezing parameter increases, both PMF and NAF increase, keeping the ratio of PMF/NAF constant, yielding an enhancement of sensitivity at the HL within a factor of root-2. Thus, the robustness of the GESP against excess noise easily exceeds that of the CESP for a broad range of values of the squeezing parameter. As such, in the context of an experimental study, it should be possible to achieve a net enhancement in sensitivity higher than that for the CESP, under typical conditions where the excess noise exceeds the unsqueezed quantum projection noise. Finally, we consider the fragility of the GESP against collisions with background particles, and show how a balance between the fragility and the robustness against excess noise would in practice determine the optimal choice of parameters for the GESP.

A point source atom interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses during the expansion of a cloud of cold atoms behaving approximately as a point source. Unlike a conventional light pulse atom interferometer, the PSI can produce a signal that corresponds to multi-axis rotation only, independent of acceleration. In addition, it can be used to measure acceleration along one direction, independent of rotation. Here, we describe a modified PSI that can be used to measure multi-axis rotation and multi-axis acceleration. Specifically, this type of PSI can be used to measure two-axes rotation around the directions perpendicular to the light pulses, as well as the acceleration in all three directions, with only one pair of Raman beams. Using two pairs of Raman beams in orthogonal directions sequentially, such a scheme would enable the realization of a complete atom interferometric inertial measurement unit.

We introduce a family of stationary coupled Sasamoto-Spohn models and show that, in the weakly asymmetric regime, they converge to the energy solution of coupled Burgers equations. Moreover, we show that any system of coupled Burgers equations satisfying the so-called trilinear condition ensuring stationarity can be obtained as the scaling limit of a suitable system of coupled Sasamoto-Spohn models. The core of our proof, which avoids the use of spectral gap estimates, consists in a second order Boltzmann-Gibbs principle for the discrete model.

The coherent population trapping (CPT) effect is used for making compact atomic clocks. There are two types of CPT clocks: the one in which the Raman beams are applied continuously and the one in which two CPT pulses separated by a dark period are applied (Ramsey scheme). It is obvious that the technique of spin squeezing can only be applied to the Ramsey CPT clock to enhance the sensitivity. However, it is not apparent how to adapt to the CPT clock the protocols for the microwave clock using one-axis-twist squeezing (OATS), since the Ramsey CPT clock is not trivially equivalent to the Ramsey microwave clock. In this paper, we show explicitly how to adapt two protocols using OATS, namely the Schr\"odinger cat state protocol (SCSP) and the generalization thereof, and the echo squeezing protocol (ESP), to the CPT clock. The ESP magnifies the phase shift by a factor of the square-root of (N/e), while the SCSP magnifies the phase shift by a factor of N/2 , making it able to achieve a higher sensitivity in the presence of excess noise., Comment: 32 pages, 5 figures

We demonstrate a new type of analysis for the DRIFT-IId directional dark matter detector using a machine learning algorithm called a Random Forest Classifier. The analysis labels events as signal or background based on a series of selection parameters, rather than solely applying hard cuts. The analysis efficiency is shown to be comparable to our previous result at high energy but with increased efficiency at lower energies. This leads to a projected sensitivity enhancement of one order of magnitude below a WIMP mass of 15 GeV c$^{-2}$ and a projected sensitivity limit that reaches down to a WIMP mass of 9 GeV c$^{-2}$, which is a first for a directionally sensitive dark matter detector.

Type 5A molecular sieves (MS) have been demonstrated to remove radon from SF$_6$ gas. This is important for ultra-sensitive SF$_6$ gas-based directional dark matter and related rare-event physics experiments, as radon can provide a source of unwanted background events. Unfortunately, commercially available sieves intrinsically emanate radon at levels not suitable for ultra-sensitive physics experiments. A method to produce a low radioactive MS has been developed in Nihon University (NU). In this work, we explore the feasibility of the NU-developed 5A type MS for use in such experiments. A comparison with a commercially available Sigma-Aldrich 5A type MS was made. The comparison was done by calculating a parameter indicating the amount of radon intrinsically emanated by the MS per unit radon captured from SF$_6$ gas. The measurements were made using a specially adapted DURRIDGE RAD7 radon detector. The NU-developed 5A MS emanated radon up to 61$\pm$9$\%$ less per radon captured (2.1$\pm$0.1)$\times 10^{-3}$, compared to the commercial Sigma-Aldrich MS (5.4$\pm$0.4)$\times 10^{-3}$, making it a better candidate for use in a radon filtration setup for future ultra-sensitive SF$_6$ gas based experiments.

A point source interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses during the expansion of a cloud of cold atoms behaving approximately as a point source. The PSI can work as a sensitive multi-axes gyroscope that can automatically filter out the signal from accelerations. The phase shift arising from rotations is proportional to the momentum transferred to each atom from the Raman pulses. Therefore, by increasing the momentum transfer, it should be possibly to enhance the sensitivity of the PSI. Here, we investigate the degree of enhancement in sensitivity that could be achieved by augmenting the PSI with large momentum transfer (LMT) employing a sequence of many Raman pulses with alternating directions. Contrary to typical approaches used for describing a PSI, we employ a model under which the motion of the center of mass of each atom is described quantum mechanically. We show how increasing Doppler shifts lead to imperfections, thereby limiting the visibility of the signal fringes, and identify ways to suppress this effect by increasing the effective, two-photon Rabi frequencies of the Raman pulses. Taking into account the effect of spontaneous emission, we show that, for a given value of the one-photon Rabi frequency, there is an optimum value for the number of pulses employed, beyond which the net enhancement in sensitivity begins to decrease. For a one-photon Rabi frequency of 200 MHz, for example, the peak value of the factor of enhancement in sensitivity is ~39, for a momentum transfer that is ~69 times as large as that for a conventional PSI. We also find that this peak value scales as the one-photon Rabi frequency to the power of 4/5.

We study the aging property for stationary models in the KPZ universality class. In particular, we show aging for the stationary KPZ fixed point, the Cole-Hopf solution to the stationary KPZ equation, the height function of the stationary TASEP, last-passage percolation with boundary conditions and stationary directed polymers in the intermediate disorder regime. All of these models are shown to display a universal aging behavior characterized by the rate of decay of their correlations. As a comparison, we show aging for models in the Edwards-Wilkinson universality class where a different decay exponent is obtained. A key ingredient to our proofs is a characteristic of space-time stationarity - covariance-to-variance reduction - which allows to deduce the asymptotic behavior of the correlations of two space-time points by the one of the variances at one point. We formulate several open problems., Comment: 34 pages. In the second version the introduction as well as the list of references were extended

We consider a one-dimensional Anderson model where the potential decays in average like $n^{-\alpha}$, $\alpha>0$. This simple model is known to display a rich phase diagram with different kinds of spectrum arising as the decay rate $\alpha$ varies. We review an article of Kiselev, Last and Simon where the authors show a.c. spectrum in the super-critical case $\alpha>\frac12$, a transition from singular continuous to pure point spectrum in the critical case $\alpha=\frac12$, and dense pure point spectrum in the sub-critical case $\alpha<\frac12$. We present complete proofs of the cases $\alpha\ge\frac12$ and simplify some arguments along the way. We complement the above result by discussing the dynamical aspects of the model. We give a simple argument showing that, despite of the spectral transition, transport occurs for all energies for $\alpha=\frac12$. Finally, we discuss a theorem of Simon on dynamical localization in the sub-critical region $\alpha<\frac12$. This implies, in particular, that the spectrum is pure point in this regime., Comment: This a reviewing paper (proceeding) of B. Simon (1982) and A. Kiselev, Y. Last, B. Simon (1998) with perspectives of O. Bourget, G. Moreno, A. Taarabt (2020). arXiv admin note: text overlap with arXiv:2001.02199

We study the spectrum and dynamics of a one-dimensional discrete Dirac operator in a random potential obtained by damping an i.i.d. environment with an envelope of type $n^{-\alpha}$ for $\alpha>0$. We recover all the spectral regimes previously obtained for the analogue Anderson model in a random decaying potential, namely: absolutely continuous spectrum in the super-critical region $\alpha>\frac12$; a transition from pure point to singular continuous spectrum in the critical region $\alpha=\frac12$; and pure point spectrum in the sub-critical region $\alpha<\frac12$. From the dynamical point of view, delocalization in the super-critical region follows from the RAGE theorem. In the critical region, we exhibit a simple argument based on lower bounds on eigenfunctions showing that no dynamical localization can occur even in the presence of point spectrum. Finally, we show dynamical localization in the sub-critical region by means of the fractional moments method and provide control on the eigenfunctions.

We consider a one-dimensional continuum Anderson model where the potential decays in average like $|x|^{-\alpha}$, $\alpha>0$. We show dynamical localization for $0<\alpha<\frac12$ and provide control on the decay of the eigenfunctions.

Sensitivities of current directional dark matter search detectors using gas time projection chambers are now constrained by target mass. A ton-scale gas TPC detector will require large charge readout areas. We present a first demonstration of a novel ThGEM-Multiwire hybrid charge readout technology which combines the robust nature and high gas gain of Thick Gaseous Electron Multipliers with lower capacitive noise of a one-plane multiwire charge readout in SF$_6$ target gas. Measurements performed with this hybrid detector show an ion drift velocity of $139~\pm~12~\text{ms}^{-1}$ in a reduced drift field $\text{E/N}$ of $93~\text{Td}~(10^{-17}~\text{V cm}^{2})$ at a gas gain of $2470\pm160$ in 20 Torr of pure SF$_\text{6}$ target gas., Comment: 17 pages, 18 figures

We consider the stationary O'Connell-Yor model of semi-discrete directed polymers in a Brownian environment in the intermediate disorder regime and show convergence of the increments of the log-partition function to the energy solutions of the stochastic Burgers equation. The proof does not rely on the Cole-Hopf transform and avoids the use of spectral gap estimates for the discrete model. The key technical argument is a second-order Boltzmann-Gibbs principle.

The design of the project named CYGNO is presented. CYGNO is a new proposal supported by INFN, the Italian National Institute for Nuclear Physics, within CYGNUs proto-collaboration (CYGNUS-TPC) that aims to realize a distributed observatory in underground laboratories for directional Dark Matter (DM) search and the identification of the coherent neutrino scattering (CNS) from the Sun. CYGNO is one of the first prototypes in the road map to 100-1000 m^3 of CYGNUs and will be located at the National Laboratory of Gran Sasso (LNGS), in Italy, aiming to make significant advances in the technology of single phase gas-only time projection chambers (TPC) for the application to the detection of rare scattering events. In particular it will focus on a read-out technique based on Micro Pattern Gas Detector (MPGD) amplification of the ionization and on the visible light collection with a sub-mm position resolution sCMOS (scientific COMS) camera. This type of readout - in conjunction with a fast light detection - will allow on one hand to reconstruct 3D direction of the tracks, offering accurate sensitivity to the source directionality and, on the other hand, a high particle identification capability very useful to distinguish nuclear recoils.

We prove the convergence of the Sasamoto-Spohn model in equilibrium to the energy solution of the stochastic Burgers equation on the whole line. The proof, which relies on the second order Boltzmann-Gibbs principle, follows the approach of \cite{GJS} and does not use any spectral gap argument.

The gas SF$_6$ has become of interest as a negative ion drift gas for use in directional dark matter searches. However, as for other targets in such searches, it is important that radon contamination can be removed as this provides a source of unwanted background events. In this work we demonstrate for the first time filtration of radon from SF$_6$ gas by using a molecular sieve. Four types of sieves from Sigma-Aldrich were investigated, namely 3{\AA}, 4{\AA}, 5{\AA} and 13X. A manufactured radon source was used for the tests. This was attached to a closed loop system in which gas was flowed through the filters and a specially adapted Durridge RAD7 radon detector. In these measurements, it was found that only the 5{\AA} type was able to significantly reduce the radon concentration without absorbing the SF$_6$ gas. The sieve was able to reduce the initial radon concentration of 3875 $\pm$ 13 Bqm$^{-3}$ in SF$_6$ gas by 87% when cooled with dry ice. The ability of the cooled 5{\AA} molecular sieve filter to significantly reduce radon concentration from SF$_6$ provides a promising foundation for the construction of a radon filtration setup for future ultra-sensitive SF$_6$ gas rare-event physics experiments., Comment: 12 pages, 10 figures

Consider directed polymers in a random environment on the complete graph of size $N$. This model can be formulated as a product of i.i.d. $N\times N$ random matrices and its large time asymptotics is captured by Lyapunov exponents and the Furstenberg measure. We detail this correspondence, derive the long-time limit of the model and obtain a co-variant distribution for the polymer path. Next, we observe that the model becomes exactly solvable when the disorder variables are located on edges of the complete graph and follow a totally asymmetric stable law of index $\alpha \in (0,1)$. Then, a certain notion of mean height of the polymer behaves like a random walk and we show that the height function is distributed around this mean according to an explicit law. Large $N$ asymptotics can be taken in this setting, for instance, for the free energy of the system and for the invariant law of the polymer height with a shift. Moreover, we give some perturbative results for environments which are close to the totally asymmetric stable laws.

Motivated by recent experiments, we consider the hydrodynamic capture of a microswimmer near a stationary spherical obstacle. Simulations of model equations show that a swimmer approaching a small spherical colloid is simply scattered. In contrast, when the colloid is larger than a critical size it acts as a passive trap: the swimmer is hydrodynamically captured along closed trajectories and endlessly orbits around the colloidal sphere. In order to gain physical insight into this hydrodynamic scattering problem, we address it analytically. We provide expressions for the critical trapping radius, the depth of the "basin of attraction," and the scattering angle, which show excellent agreement with our numerical findings. We also demonstrate and rationalize the strong impact of swimming-flow symmetries on the trapping efficiency. Finally, we give the swimmer an opportunity to escape the colloidal traps by considering the effects of Brownian, or active, diffusion. We show that in some cases the trapping time is governed by an Ornstein-Uhlenbeck process, which results in a trapping time distribution that is well-approximated as inverse-Gaussian. The predictions again compare very favorably with the numerical simulations. We envision applications of the theory to bioremediation, microorganism sorting techniques, and the study of bacterial populations in heterogeneous or porous environments.

We compute the fluctuation exponents for a solvable model of one-dimensional directed polymers in random environment in the intermediate regime. This regime corresponds to taking the inverse temperature to zero with the size of the system. The exponents satisfy the KPZ scaling relation and coincide with physical predictions. In the critical case, we recover the fluctuation exponents of the Cole-Hopf solution of the KPZ equation in equilibrium and close to equilibrium., Comment: 30 pages

We give a new proof of the fact that the solutions of the stochastic heat equation, started with non-negative initial conditions, are strictly positive at positive times. The proof uses concentration of measure arguments for discrete directed polymers in Gaussian environments, originated in M. Talagrand's work on spin glasses and brought to directed polymers by Ph. Carmona and Y. Hu. We also get slightly improved bounds on the lower tail of the solutions of the stochastic heat equation started with a delta initial condition., Comment: Minor modifications, near to final version, to appear in AOP

We study the scaling limit of the spectrum of the \beta-Jacobi ensemble at the soft-edge and hard-edge for general values of \beta. We show that the limiting point processes correspond respectively to the stochastic Airy and Bessel point processes introduced in Ramirez-Rider-Virag and Ramirez-Rider., Comment: Minor changes

The model of Brownian Percolation has been introduced as an approximation of discrete last-passage percolation models close to the axis. It allowed to compute some explicit limits and prove fluctuation theorems for these, based on the relations between the Brownian percolation and random matrices. Here, we present two approaches that allow to treat discrete asymmetric models of directed polymers. In both cases, the behaviour is universal, meaning that the results do not depend on the precise law of the environment as long as it satisfies some natural moment assumptions. First, we establish an approximation of asymmetric discrete directed polymers in random environments at very high temperature by a continuous-time directed polymers model in a Brownian environment, much in the same way than the last passage percolation case. The key ingredient is a strong embedding argument developed by K\'omlos, Major and T\'usnady. Then, we study the partition function of a $1+1$-dimensional directed polymer in a random environment with a drift tending to infinity. We give an explicit expression for the free energy based on known asymptotics for last-passage percolation and compute the order of the fluctuations of the partition function. We conjecture that the law of the properly rescaled fluctuations converges to the GUE Tracy-Widom distribution.