Abstract
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 $E \lambda_i > 1$.
Citation
Dayue Chen. Thomas M. Liggett. "Finite Reversible Nearest Particle Systems in Inhomogeneous and Random Environments." Ann. Probab. 20 (1) 152 - 173, January, 1992. https://doi.org/10.1214/aop/1176989922
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