Invariance principle for the random conductance model with dynamic bounded conductances

Andres, Sebastian

Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 2, pp. 352-374.

Nous étudions une chaîne de Markov en temps continu $X$ dans un environnement dynamique de conductances aléatoires dans ${\mathbb{Z}}^d$. 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.

We study a continuous time random walk $X$ in an environment of dynamic random conductances in ${\mathbb{Z}}^d$. 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.

Classification : 60K37, 60F17, 82C41
Mots clés : random conductance model, dynamic environment, invariance principle, ergodic, corrector, point of view of the particle, stochastic interface model

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