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 $E \lambda_i > 1$.
Publié le : 1992-01-14
Classification:
Nearest particle systems,
random environment,
survival,
Dirichlet principle,
60K35
@article{1176989922,
author = {Chen, Dayue and Liggett, Thomas M.},
title = {Finite Reversible Nearest Particle Systems in Inhomogeneous and Random Environments},
journal = {Ann. Probab.},
volume = {20},
number = {4},
year = {1992},
pages = { 152-173},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989922}
}
Chen, Dayue; Liggett, Thomas M. Finite Reversible Nearest Particle Systems in Inhomogeneous and Random Environments. Ann. Probab., Tome 20 (1992) no. 4, pp. 152-173. http://gdmltest.u-ga.fr/item/1176989922/