Invariance principle for the random conductance model with dynamic bounded conductances
Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 2, pp. 352-374.

We study a continuous time random walk X in an environment of dynamic random conductances in d . We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched invariance principle for X, and obtain Green’s functions bounds and a local limit theorem. We also discuss a connection to stochastic interface models.

Nous étudions une chaîne de Markov en temps continu X dans un environnement dynamique de conductances aléatoires dans d . Nous supposons que les conductances sont stationnaires ergodiques, uniformément positives et polynomialement mélangeantes en espace et en temps. Nous montrons un principe d’invariance << quenched >> pour X, et nous obtenons des bornes sur les fonctions de Green et un théorème limite local. Nous discutons aussi les liens avec les modèles d’interfaces aléatoires.

DOI: 10.1214/12-AIHP527
Classification: 60K37, 60F17, 82C41
Keywords: random conductance model, dynamic environment, invariance principle, ergodic, corrector, point of view of the particle, stochastic interface model
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Andres, Sebastian. Invariance principle for the random conductance model with dynamic bounded conductances. Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 2, pp. 352-374. doi : 10.1214/12-AIHP527. http://archive.numdam.org/articles/10.1214/12-AIHP527/

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