Quelques compléments sur le processus des misanthropes et le processus ''zéro-range''
type: Item
instance of: scholarly article
title: Quelques compléments sur le processus des misanthropes et le processus ''zéro-range''
zbMATH Open document ID: 0581.60093
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77263
review text: The misanthrope process is an infinite particle system on the lattice \({\mathbb{Z}}^ d\), which was introduced by the second author, Z. Wahrscheinlichkeitstheor. Verw. Geb. 70, 509-523 (1985; Zbl 0554.60097)]. It generalizes the zero range process. In the mentioned paper invariant measures and convergence to them were studied. The present paper gives two additional results for the one-dimensional case. It is shown for the nearest neighbour misanthrope process that, if the initial distribution is translation invariant, ergodic and has a finite density, then the process converges to the ergodic invariant measure with the same density. Furthermore it is proved that, if the expectation of the jumps is zero, then all invariant measures are translation invariant. The proofs are based on coupling techniques.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 3930101
zbMATH Keywords: infinite particle system
zbMATH Keywords: invariant measures
zbMATH Keywords: nearest neighbour misanthrope process
zbMATH Keywords: coupling techniques
author: Enrique Daniel Andjel
author: Christiane Cocozza-Thivent
author: M. Roussignol
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3930101