An estimate of the spectral gap for zero-range-exclusion dynamics
type: Item
instance of: scholarly article
title: An estimate of the spectral gap for zero-range-exclusion dynamics
zbMATH Open document ID: 1091.60510
author: Yukio Nagahata
author: Kohei Uchiyama
published in: Osaka Journal of Mathematics
publication date: 2005-03-18T00:00:00Z
review text: The authors consider a Markovian system of particles carrying energy in \(\mathbb{Z}^d\). The dynamics is a combination of an exclusion process for the particles and a zero-range process for their energy. The process has two conserved quantities, the number of particles and the total energy. In this paper an estimate of the spectral gap is derived. It is proved that for the process in a cube of width \(n\) the spectral gap is bounded below by \(Cn^{-2}\), where \(C\) is independent of \(n\), but depends on the two local conserved quantities, the number of particles per site and the energy per particle. The estimation of the spectral gap of similar models is commonly reduced to two steps: an estimate of the spectral gap of the corresponding mean field dynamics and a moving-particle lemma. For the present model the former is obtained by an adaptation of the methods of \textit{C. Landim, S. Sethuraman} and \textit{S. Varadhan} [Ann. Probab. 24, No. 4, 1871--1902 (1996; Zbl 0870.60095)], but the moving-particle lemma is not so simple as for exclusion or zero-range processes and causes the dependence of the constant \(C\) on the conserved quantities.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82C22
zbMATH DE Number: 2147095
zbMATH Keywords: exclusion process
zbMATH Keywords: zero-range process
zbMATH Keywords: spectral gap
zbMATH Keywords: moving-particle lemma
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2147095