Related papers: Hydrodynamic limit for asymmetric simple exclusion…
We develop a hydrodynamic theory for a height-dependent version of the totally asymmetric simple exclusion process in which the jump rate at a growth site is sampled from a macroscopic two-dimensional speed function evaluated at the spatial…
The purpose of this article is to provide a simple proof of the hydrodynamic and hydrostatic behavior of the SSEP in contact with slowed reservoirs which inject and remove particles in a finite size windows at the extremities of the bulk.…
We derive the Euler (hyperbolic) hydrodynamic limit for the directed exclusion process (DEP), a one-dimensional conservative interacting particle system that preserves particle-hole symmetry while breaking left-right symmetry. The proof…
We consider the hydrodynamic scaling behavior of the mass density with respect to a general class of mass conservative interacting particle systems on ${\mathbb Z}^n$, where the jump rates are asymmetric and long-range of order…
We study the hydrodynamic limit for some conservative particle systems with degenerate rates, namely with nearest neighbor exchange rates which vanish for certain configurations. These models belong to the class of {\sl kinetically…
In this article, we consider the ABC model in contact with slow/fast reservoirs. In this model, there is at most one particle per site, which can be of type $\alpha\in\{A,B,C\}$ and particles exchange positions in the discrete set of points…
In this paper we focus on the open symmetric exclusion process with parameter $m$ (open SEP($m/2$)), which allows $m$ particles each site and has an open boundary. We generalize the result about hydrodynamic limit for the open SEP$(m/2)$…
The collective non-equilibrium dynamics of multi-component mixtures of interacting active (self-propelled) and passive (diffusive) particles have garnered great interest in the physics community. However, the mathematical understanding of…
We study the steady state of the two-species Asymmetric Simple Exclusion Process (ASEP) with open boundary conditions. The matrix product method works for the determination of the stationary probability distribution. Several physical…
We study the hydrodynamic limit for a model of symmetric exclusion processes with heavy-tailed long jumps and in contact with infinitely extended reservoirs. We show how the corresponding hydrodynamic equations are affected by the…
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…
This report is the foreword of a series dedicated to stochastic deformations of curves. Problems are set in terms of exclusion processes, the ultimate goal being to derive hydrodynamic limits for these systems after proper scalings. In this…
We revisit in this short article the hydrostatic limit for the exclusion process with slow boundary. The original proof of this result relies on estimates of the correlation functions. We achieve the same result based on analysis of two…
We consider the symmetric exclusion process with jumps given by a symmetric, translation invariant, transition probability $p(\cdot)$. The process is put in contact with stochastic reservoirs whose strength is tuned by a parameter…
We consider continuous-time random walks on a random locally finite subset of $\mathbb{R}^d$ with random symmetric jump probability rates. The jump range can be unbounded. We assume some second--moment conditions and that the above…
We consider the large deviations from the hydrodynamic limit of the Totally Asymmetric Simple Exclusion Process (TASEP). This problem was studied in Jensen (2000) and Varadhan (2004) and was shown to be related to entropy production in the…
We consider the totally asymmetric simple exclusion process (TASEP) on a periodic one-dimensional lattice of L sites. Using Bethe ansatz, we derive parametric formulas for the eigenvalues of its generator in the thermodynamic limit. This…
We analyse the hydrodynamical behavior of the long jumps symmetric exclusion process in the presence of a slow barrier. The jump rates are given by a symmetric transition probability $p(\cdot)$ with infinite variance. When jumps occur from…
We study the speed of convergence to equilibrium for the asymmetric simple exclusion process (ASEP) on a finite interval with one open boundary. We provide sharp estimates on the total-variation distance from equilibrium and verify that the…
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,…