Stationary measures for an exclusion process on one-dimensional lattices with infinitely many hopping sites
type: Item
instance of: scholarly article
title: Stationary measures for an exclusion process on one-dimensional lattices with infinitely many hopping sites
zbMATH Open document ID: 0615.60097
author: Hirotake Yaguchi
published in: Hiroshima Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Stationary measures for the following exclusion process on one- dimensional lattices with discrete time parameter are considered: As time increases from t to \(t+1\), each particle which locates at the site i moves to the site i-1 independently with probability \(\alpha\) \((0<\alpha <1/2)\) iff the site i-1 is unoccupied. It is known that the stationary measures for the process are the convex combinations of a family of nearest neighbor Gibbs states (renewal measures) \(\{\pi_{\gamma}:\) \(0<\gamma <\infty \}\) and trivial Dirac measures \(\{\pi_ 0,\pi_{\infty},\Theta_ n,n\in {\mathbb{Z}}\}\). Concerning the stochastic property of a tagged particle under the time evolution with respect to the stationary state \(\pi_{\gamma}\), it is shown that the position of tagged particle \(\{\) r(t), \(t=0,1,2,...\}\) has independent increments, i.e., \(\{\) r(t)-r(t-1)\(\}\) is a Bernoulli sequence, and so a central limit theorem holds. By applying a simple limiting procedure to our process we can obtain a usual simple exclusion process with continuous time parameter.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 3996824
zbMATH Keywords: infinite particle systems
zbMATH Keywords: Gibbs states
zbMATH Keywords: Dirac measures
zbMATH Keywords: tagged particle
zbMATH Keywords: central limit theorem
zbMATH Keywords: exclusion process
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3996824