The philosophers' process: An ergodic reversible nearest particle system
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).
scientific article; zbMATH DE number 436544