Related papers: Symmetric simple exclusion process with free bound…
We consider the totally asymmetric simple exclusion process (TASEP) starting with a shock discontinuity at the origin, with asymptotic densities $\lambda$ to the left of the origin and $\rho$ to the right of it and $\lambda<\rho$. We find…
We consider the one-dimensional totally asymmetric simple exclusion process (TASEP) with position-dependent hopping rates. The problem is solved,in a mean field/adiabatic approximation, for a general (smooth) form of spatial rate variation.…
We consider a branching-selection system in $\mathbb {R}$ with $N$ particles which give birth independently at rate 1 and where after each birth the leftmost particle is erased, keeping the number of particles constant. We show that, as…
We consider the symmetric simple exclusion process in $\mathbb Z^d$ with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the self-duality of the process,…
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 consider the asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$ with an initial data such that in the large time particle density $\rho(\cdot)$ a discontinuity at the origin is created, where the value of $\rho$ jumps from zero…
In this paper, we prove the hydrodynamic limit for the ergodic dynamics of the Facilitated Exclusion Process with closed boundaries in the symmetric, asymmetric and weakly asymmetric regimes. For this, we couple it with a Simple Exclusion…
We consider a two-component asymmetric simple exclusion process (ASEP) on a finite lattice with reflecting boundary conditions. For this process, which is equivalent to the ASEP with second-class particles, we construct the representation…
We introduce and analyse a two-sided branching-selection particle system which generalises the well-known $N$-particle branching Brownian motion ($N$-BBM) model, which we call the $(N,p)$-BBM, where either the leftmost or rightmost particle…
We study a generalization of the asymmetric simple inclusion process (ASIP) on a periodic one-dimensional lattice, where the integers in the particles rates are deformed to their $t$-analogues. We call this the $(q, t, \theta)$~ASIP, where…
We introduce a class of facilitated asymmetric exclusion processes in which particles are pushed by neighbors from behind. For the simplest version in which a particle can hop to its vacant right neighbor only if its left neighbor is…
In this paper we review some results on time-homogeneous birth-death processes. Specifically, for truncated birth-death processes with two absorbing or two reflecting endpoints, we recall the necessary and sufficient conditions on the…
We investigate the stationary distribution of asymmetric and weakly asymmetric simple exclusion processes with open boundaries. We project the stationary distribution onto a subinterval, whose size is allowed to grow with the length of the…
The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional dynamics of interacting particles on a $1$D-lattice that is much used in systems biology and statistical physics. Its master equation…
We analyze the non-equilibrium fluctuations of the partial symmetric simple exclusion process, SEP($\alpha$), which allows at most $\alpha \in \mathbb{N}$ particles per site, and we put it in contact with stochastic reservoirs whose…
The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by Bethe ansatz and put emphasis on the algebraic properties of this model.…
We formulate and analyze the steady-state behavior of totally asymmetric simple exclusion processes (TASEPs) that contain periodically varying movement rates. In our models, particles at a majority sites hop to the right with rate $p_1$…
The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary…
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…
Research in combinatorics has often explored the asymmetric simple exclusion process (ASEP). The ASEP, inspired by examples from statistical mechanics, involves particles of various species moving around a lattice. With the traditional ASEP…