The philosophers' process: An ergodic reversible nearest particle system
type: Item
instance of: scholarly article
title: The philosophers' process: An ergodic reversible nearest particle system
zbMATH Open document ID: 0798.60086
author: Bernard Ycart
published in: The Annals of Applied Probability
publication date: 1993-10-28T00:00:00Z
review text: The author studies an interacting particle system which is suggested by an extension of the dining philosophers' problem introduced by \textit{E. W. Dijkstra} [Commun. ACM 11, 341-346 (1968; Zbl 0164.187)]. Assume that the philosophers are placed on the vertices of an undirected graph \(G\) with bounded degree. A philosopher can eat only if all his neighbours are thinking. He will begin eating after an exponential time with parameter \(\lambda\), if he still can. A philosopher eating will stop after an exponential time with parameter \(\mu\). The main result of the present paper is that in the case \(G=Z^ 1\) the process is ergodic (its stationary renewal measure being its unique reversible measure).
reviewed by: Klaus Schürger
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 436544
zbMATH Keywords: interacting particle system
zbMATH Keywords: stationary renewal measure
zbMATH Keywords: unique reversible measure
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177005428
OpenAlex ID: W2021436164
DOI: 10.1214/AOAP/1177005428
description: scientific article; zbMATH DE number 436544