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January, 1992 Finite Reversible Nearest Particle Systems in Inhomogeneous and Random Environments
Dayue Chen, Thomas M. Liggett
Ann. Probab. 20(1): 152-173 (January, 1992). DOI: 10.1214/aop/1176989922


In this article we propose and study finite reversible nearest particle systems in inhomogeneous and random environments. Using the Dirichlet principle and the ergodic theorem we prove that a finite reversible nearest particle system in a random environment determined by an i.i.d. sequence $\lambda_i$ survives if $E \log \lambda_i > 0$ and dies out if $E\lambda_i < 1$. Some discussion is provided to show that both survival and extinction may happen when $E \log \lambda_i < 0$ and $E \lambda_i > 1$.


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Dayue Chen. Thomas M. Liggett. "Finite Reversible Nearest Particle Systems in Inhomogeneous and Random Environments." Ann. Probab. 20 (1) 152 - 173, January, 1992.


Published: January, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0753.60099
MathSciNet: MR1143416
Digital Object Identifier: 10.1214/aop/1176989922

Primary: 60K35

Keywords: Dirichlet principle , nearest particle systems , random environment , survival

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 1 • January, 1992
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