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We consider the large deviations of the hydrodynamic rescaling of the zero-range process on $\mathbb{Z}^d$ in any dimension $d\ge 1$. Under mild and canonical hypotheses on the local jump rate, we obtain matching upper and lower bounds,…

Probability · Mathematics 2025-08-01 Benjamin Fehrman , Benjamin Gess , Daniel Heydecker

We consider the facilitated exclusion process, which is a nonergodic, kinetically constrained exclusion process. We show that in the hydrodynamic limit, its macroscopic behavior is governed by a free boundary problem. The particles evolve…

Probability · Mathematics 2021-03-17 Oriane Blondel , Clément Erignoux , Marielle Simon

We construct a non reversible exclusion process with Bernoulli product invariant measure and having, in the diffusive hydrodynamic scaling, a non symmetric diffusion matrix, that can be explicitly computed. The antisymmetric part does not…

Probability · Mathematics 2025-02-18 Leonardo De Carlo , Davide Gabrielli , Patrícia Gonçalves

We study general zero range processes with different types of particles on a d-dimensional lattice with periodic boundary conditions. A necessary and sufficient condition on the jump rates for the existence of stationary product measures is…

Statistical Mechanics · Physics 2018-04-26 Stefan Grosskinsky , Herbert Spohn

We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…

Probability · Mathematics 2023-11-22 Jean Bérard , Brieuc Frénais

In this article we analyse the hydrodynamical behavior of the symmetric exclusion process with long jumps and in the presence of a slow barrier. The jump rates for fast bonds are given by a transition probability $p(\cdot)$ which is…

Probability · Mathematics 2022-06-24 Pedro Cardoso , Patrícia Gonçalves , Byron Jiménez-Oviedo

We extend the usual hydrodynamic description of the symmetric exclusion process by keeping track of collision events corresponding to jumps into already occupied sites, thereby quantifying the dissipated part of the microscopic activity…

Probability · Mathematics 2025-12-24 Mario Ayala , D. R. Michiel Renger

An infinite particle system of independent jumping particles in infinite volume is considered. Their construction is recalled,further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second…

We study the symmetric Dyson exclusion process (SDEP) - a lattice gas with exclusion and long-range, Coulomb-type interactions that emerge both as the maximal-activity limit of the symmetric exclusion process and as a discrete version of…

Statistical Mechanics · Physics 2026-05-20 Ali Zahra , Jerome Dubail , Gunter M. Schütz

A fundamental problem of non-equilibrium statistical mechanics is the derivation of macroscopic transport equations in the hydrodynamic limit. The rigorous study of such limits requires detailed information about rates of convergence to…

Mathematical Physics · Physics 2015-05-30 Alexander Grigo , Konstantin Khanin , Domokos Szasz

We consider the asymmetric simple exclusion process (ASEP) on the one-dimensional finite lattice $\{1,2,\ldots,N\}$. The particles can be created/annihilated at the boundaries with given rates. These rates are $L^\infty$ functions of time…

Probability · Mathematics 2024-08-27 Lu Xu

We consider a lattice model of active matter with exclusion and derive its hydrodynamic description exactly. The hydrodynamic limit leads to an integro-differential equation for the density of particles with a given orientation. Volume…

Mathematical Physics · Physics 2023-10-31 James Mason , Clement Erignoux , Robert Jack , Maria Bruna

We obtain the hydrodynamic limit of symmetric long-jumps exclusion in $\mathbb{Z}^d$ (for $d \geq 1$), where the jump rate is inversely proportional to a power of the jump's length with exponent $\gamma+1$, where $\gamma \geq 2$. Moreover,…

Probability · Mathematics 2024-06-11 Pedro Cardoso , Patrícia Gonçalves , Byron Jiménez-Oviedo

The exclusion process in which particles may jump any distance l>=1 with the probability that decays as l^-(1+sigma) is studied from coarse-grained equation for density profile in the limit when the lattice spacing goes to zero. For…

Statistical Mechanics · Physics 2008-05-16 J. Szavits-Nossan , K. Uzelac

The Markov dynamics of interlaced particle arrays, introduced by A. Borodin and P. Ferrari in arXiv:0811.0682, is a classical example of (2+1)-dimensional random growth model belonging to the so-called Anisotropic KPZ universality class. In…

Probability · Mathematics 2022-03-01 Vincent Lerouvillois , Fabio Lucio Toninelli

This article considers some classes of models dealing with the dynamics of discrete curves subjected to stochastic deformations. It turns out that the problems of interest can be set in terms of interacting exclusion processes, the ultimate…

Probability · Mathematics 2012-01-26 Guy Fayolle , Cyril Furtlehner

The hydrodynamic description of probabilistic ballistic annihilation, for which no conservation laws hold, is an intricate problem with hard sphere-like dynamics for which no exact solution exists. We consequently focus on simplified…

Statistical Mechanics · Physics 2007-05-23 Francois Coppex , Michel Droz , Emmanuel Trizac

We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…

Probability · Mathematics 2024-05-07 Vadim Malyshev , Mikhail Menshikov , Serguei Popov , Andrew Wade

We consider the generalized hydrodynamics including the recently introduced diffusion term for an initially inhomogeneous state in the Lieb-Liniger model. We construct a general solution to the linearized hydrodynamics equation in terms of…

Quantum Gases · Physics 2020-01-16 Miłosz Panfil , Jacek Pawełczyk

We study the large space and time scale behavior of a totally asymmetric, nearest-neighbor exclusion process in one dimension with random jump rates attached to the particles. When slow particles are sufficiently rare the system has a phase…

Probability · Mathematics 2007-05-23 Ilie Grigorescu , Min Kang , Timo Seppalainen