Related papers: Concurrent Donsker-Varadhan and hydrodynamical lar…
We study the condensation phenomenon for the invariant measures of the mean-field model of reversible coagulation-fragmentation processes conditioned to a supercritical density of particles. It is shown that when the parameters of the…
The steady-state currents and densities of a one-dimensional totally asymmetric exclusion process (TASEP) with particles that occlude an integer number ($d$) of lattice sites are computed using various mean field approximations and Monte…
We consider two-species exclusion processes on the d-dimensional discrete torus taking the effects of exchange, creation and annihilation into account. The model is, in general, of nongradient type. We prove that the (charged) particle…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
In this paper we introduce a topology under which the pair empirical measure of a large class of random walks satisfies a strong Large Deviation principle. The definition of the topology is inspired by the recent article by Mukherjee and…
We consider the one dimensional asymmetric exclusion process with particle injection and extraction at two boundaries. The model is known to exhibit four distinct phases in its stationary state. We analyze the current statistics at the…
We prove here the validity of a large deviation principle for the family of invariant measures associated to a two dimensional Navier-Stokes equation on a torus, perturbed by a smooth additive noise.
We introduce a variational time discretization for the multi-dimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each timestep requires the minimization of a functional measuring the…
Consider an intersection measure $\ell_t ^{\mathrm{IS}}$ of $p$ independent (possibly different) $m$-symmetric Hunt processes up to time $t$ in a metric measure space $E$ with a Radon measure $m$. We derive a Donsker-Varadhan type large…
We introduce the headway exclusion process which is an exclusion process with $N$ particles on the one-dimensional discrete torus with $L$ sites with jump rates that depend only on the distance to the next particle in the direction of the…
The long time behavior of a couple of interacting asymmetric exclusion processes of opposite velocities is investigated in one space dimension. We do not allow two particles at the same site, and a collision effect (exchange) takes place…
The aim of this paper is to develop tractable large deviation approximations for the empirical measure of a small noise diffusion. The starting point is the Freidlin-Wentzell theory, which shows how to approximate via a large deviation…
Current is a characteristic feature of nonequilibrium systems. In stochastic systems, these currents exhibit fluctuations constrained by the rate of dissipation in accordance with the recently discovered thermodynamic uncertainty relation.…
In this paper, we prove a central limit theorem and establish a moderate deviation principle for 2D stochastic hydrodynamical type systems with multiplicative noise in unbounded domains, which covers 2D Navier-Stokes equations, 2D MHD…
In this thesis, we consider one of the most popular models of non-equilibrium statistical physics: the Asymmetric Simple Exclusion Process, in which particles jump stochastically on a one-dimensional lattice, between two reservoirs at fixed…
The additivity principle allows a calculation of current fluctuations and associated density profiles in large diffusive systems. In order to test its validity in the weakly asymmetric exclusion process with open boundaries, we use a…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
In this paper, we consider the convergence rate with respect to the Wasserstein distance in the invariance principle for sequential dynamical systems. We utilize and modify the techniques previously employed for stationary sequences to…
This paper considers the asymptotic limit of small aspect ratio between vertical and horizontal spatial scales for viscous isothermal compressible flows. In particular, it is observed that fast vertical acoustic waves arise and induce an…
We consider a system of $N^{d}$ spins in random environment with a random local mean field type interaction. Each spin has a fixed spatial position on the torus $\mathbb{T}^{d}$, an attached random environment and a spin value in…