Invariant measures for linear infinite particle systems with values in \([0,\infty)^ S\).
type: Item
instance of: scholarly article
title: Invariant measures for linear infinite particle systems with values in \([0,\infty)^ S\).
zbMATH Open document ID: 0657.60125
author: Ellen Saada
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77334
review text: For the linear infinite particle systems with values in \([0,\infty)^ S\) whose transition rates are translation invariant, the set (\({\mathcal P}\cap {\mathcal S})_ e\) of extremal invariant and translation invariant probability measures was known. We prove that under additional assumptions on the transition rates (including the recurrence of a transition probability associated to the process), \({\mathcal P}_ e=({\mathcal P}\cap {\mathcal S})_ e.\) We apply this result to some examples, and we finally obtain \({\mathcal P}_ e\) in a simple way for the symmetric simple exclusion process in the irreducible and recurrent case.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4074161
zbMATH Keywords: linear infinite particle systems
zbMATH Keywords: extremal invariant and translation invariant probability measures
zbMATH Keywords: recurrence
zbMATH Keywords: symmetric simple exclusion process
zbMATH Keywords: irreducible
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4074161