Some properties of \(k\)-step exclusion processes
type: Item
instance of: scholarly article
title: Some properties of \(k\)-step exclusion processes
zbMATH Open document ID: 0953.60091
published in: Journal of Statistical Physics
publication date: 2001-01-22T00:00:00Z
review text: The author studies a generalization of the well-known simple exclusion process. Roughly speaking, the process evolves as follows. On each site, there is a clock that rings with exponential rate \(1\). The clocks at different sites are iid. If a particle is at present at site \(x\) when the clock associated to this site rings, then the particle occupies the first vacant site encountered in the sequence \((X_n)_{1\leq n \leq k}\), where \(\{X_n\}_n\) is a Markov chain starting from \(x\) (the Markov chain is assumed to be a random walk, or reversible and positive recurrent). If no empty site is encountered during these \(k\) attempts, then the movement is cancelled and the particle stays at \(x\). As in the original situation, the author studies the structure of the invariant measures, the law of large numbers for two classes of particles (the first class is the standard tagged one).
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 1370579
zbMATH Keywords: interacting particle systems
zbMATH Keywords: tagged particle
zbMATH Keywords: \(k\)-steps exclusion process
zbMATH Keywords: invariant measures
author: Hervé Guiol
reviewed by: Mu-Fa Chen
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1370579