Asymptotic behaviour of a tagged particle in an inhomogeneous zero-range process
type: Item
instance of: scholarly article
title: Asymptotic behaviour of a tagged particle in an inhomogeneous zero-range process
zbMATH Open document ID: 0935.60081
DOI: 10.1016/S0304-4149(98)00040-4
author: Paola Siri
published in: Stochastic Processes and their Applications
publication date: 1999-11-18T00:00:00Z
review text: A spatially inhomogeneous zero-range jump process in \(\mathbb Z^d\) is investigated. The jumps are described by a symmetric random walk with the rate depending on the number of particles at \(x\in \mathbb Z^d\) and also on the site \(x\) itself. Roughly speaking, the main result states that the process describing the behaviour of a tagged particle, when rescaling the space by \(\frac {1}{\varepsilon}\) and the time by \(\frac {1}{\varepsilon ^2}\), tends to a diffusion on the \(d\)-dimensional torus when \(\varepsilon \) tends to zero. Ergodicity of some auxiliary Markov processes is used to deduce that a weak limit of the rescaled processes is the solution of a suitable martingale problem.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82C22
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 1364505
zbMATH Keywords: infinite particle systems
zbMATH Keywords: zero-range process
zbMATH Keywords: tagged particle
zbMATH Keywords: invariance principle
reviewed by: Petr Holický
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1364505