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May, 1993 The Philosophers' Process: An Ergodic Reversible Nearest Particle System
Bernard Ycart
Ann. Appl. Probab. 3(2): 356-363 (May, 1993). DOI: 10.1214/aoap/1177005428

Abstract

This paper studies the philosophers' process, introduced in the finite case of Zenie after Dijkstra's dining philosophers' problem and in different contexts by Suhov and Kelly. This process is presented as a nearest particle system on $\mathbb{Z}$, where a configuration may flip from 0 to 1 at one site $x$ only if it is null for the two neighbors of $x$. It flips from 1 to 0 at a constant rate. The model is proved to be ergodic and reversible, and its stationary measure is explicitly characterized. In the finite case (configurations on $\mathbb{Z}/L\mathbb{Z})$, an explicit expression for the stationary measure is given.

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Bernard Ycart. "The Philosophers' Process: An Ergodic Reversible Nearest Particle System." Ann. Appl. Probab. 3 (2) 356 - 363, May, 1993. https://doi.org/10.1214/aoap/1177005428

Information

Published: May, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0798.60086
MathSciNet: MR1221156
Digital Object Identifier: 10.1214/aoap/1177005428

Subjects:
Primary: 60K35

Keywords: Philosophers' process , reversible nearest particle system

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.3 • No. 2 • May, 1993
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