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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…

Probability · Mathematics 2025-08-19 V. Belitsky , N. P. N. Ngoc , G. M. Schütz

We prove a large deviations principle for the empirical measure of the one dimensional symmetric simple exclusion process in contact with reservoirs. The dynamics of the reservoirs is slowed down with respect to the dynamics of the system,…

Probability · Mathematics 2021-07-16 Tertuliano Franco , Patrícia Gonçalves , Adriana Neumann

We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…

Statistical Mechanics · Physics 2015-06-24 Guy Fayolle , Cyril Furtlehner

We consider the simple exclusion process in the integer segment $ [1, N]$ with $k\le N/2$ particles and spatially inhomogenous jumping rates. A particle at site $x\in [ 1, N]$ jumps to site $x-1$ (if $x\ge 2$) at rate $1-\omega_x$ and to…

Probability · Mathematics 2024-02-20 Hubert Lacoin , Shangjie Yang

We consider the one dimensional symmetric simple exclusion process with a slow bond. In this model, particles cross each bond at rate $N^2$, except one particular bond, the slow bond, where the rate is $N$. Above, $N$ is the scaling…

Probability · Mathematics 2021-03-17 Xiaofeng Xue , Linjie Zhao

We consider an exclusion process with finite-range interactions in the microscopic interval $[0,N]$. The process is coupled with the simple symmetric exclusion processes in the intervals $[-N,-1]$ and $[N+1,2N]$, which simulate reservoirs.…

Mathematical Physics · Physics 2020-04-22 Pasha Tkachov

We study a totally asymmetric simple exclusion process where jumps happen at rate one, except at the origin where the rate is lower. We prove a hydrodynamic scaling limit to a macroscopic profile described by a variational formula. The…

Probability · Mathematics 2007-05-23 Timo Seppalainen

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

We consider an exclusion process with long jumps in the box $\Lambda\_N=\{1, \ldots,N-1\}$, for $N \ge 2$, in contact with infinitely extended reservoirs on its left and on its right. The jump rate is described by a transition probability…

Probability · Mathematics 2021-08-09 Cedric Bernardin , Patricia Goncalves , Byron Oviedo Jimenez

In this paper we consider three classes of interacting particle systems on $\mathbb Z$: independent random walks, the exclusion process, and the inclusion process. We allow particles to switch their jump rate (the rate identifies the type…

We consider a one-dimensional simple symmetric exclusion process in equilibrium, constituting a dynamic random environment for a nearest-neighbor random walk that on occupied/vacant sites has two different local drifts to the right. We…

Probability · Mathematics 2012-02-28 Luca Avena , Renato dos Santos , Florian Völlering

We investigate a novel variant of the exclusion process in which particles perform asymmetric nearest-neighbor jumps across a bond \((k, k+1)\) only if the preceding site \((k-1)\) is unoccupied. This next-nearest-neighbor constraint…

Statistical Mechanics · Physics 2025-09-19 Gunter Schutz , Ali Zahra

We study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries, where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely…

Statistical Mechanics · Physics 2007-08-23 Robert Juhasz

Consider a system of particles performing nearest neighbor random walks on the lattice $\ZZ$ under hard--core interaction. The rate for a jump over a given bond is direction--independent and the inverse of the jump rates are i.i.d. random…

Probability · Mathematics 2007-09-05 A. Faggionato , M. Jara , C. Landim

We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we…

Probability · Mathematics 2023-12-04 Chiara Franceschini , Patrícia Gonçalves , Federico Sau

We study the non-equilibrium stationary fluctuations of a symmetric zero-range process on the discrete interval $\{1, \ldots, N-1\}$ coupled to reservoirs at sites $1$ and $N-1$, which inject and remove particles at rates proportional to…

Probability · Mathematics 2026-01-09 Patrícia Gonçalves , Adriana Neumann , Maria Chiara Ricciuti

Consider "Frozen Random Walk" on $\mathbb{Z}$: $n$ particles start at the origin. At any discrete time, the leftmost and rightmost $\lfloor{\frac{n}{4}}\rfloor$ particles are "frozen" and do not move. The rest of the particles in the "bulk"…

Probability · Mathematics 2015-09-02 Laura Florescu , Shirshendu Ganguly , Yuval Peres , Joel Spencer

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

We study the hydrodynamic limit for a periodic $1$-dimensional exclusion process with a dynamical constraint, which prevents a particle at site $x$ from jumping to site $x\pm1$ unless site $x\mp1$ is occupied. This process with degenerate…

Probability · Mathematics 2020-10-23 Oriane Blondel , Clément Erignoux , Makiko Sasada , Marielle Simon

We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case the accumulated…

Disordered Systems and Neural Networks · Physics 2009-11-10 R. Juhasz , L. Santen , F. Igloi