Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Invariance principle for the random conductance model with dynamic bounded conductances

Sebastian Andres

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Abstract

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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 50, Number 2 (2014), 352-374.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1395856131

Digital Object Identifier
doi:10.1214/12-AIHP527

Mathematical Reviews number (MathSciNet)
MR3189075

Zentralblatt MATH identifier
1290.60109

Subjects
Primary: 60K37: Processes in random environments 60F17: Functional limit theorems; invariance principles 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

Keywords
Random conductance model Dynamic environment Invariance principle Ergodic Corrector Point of view of the particle Stochastic interface model

Citation

Andres, Sebastian. Invariance principle for the random conductance model with dynamic bounded conductances. Ann. Inst. H. Poincaré Probab. Statist. 50 (2014), no. 2, 352--374. doi:10.1214/12-AIHP527. https://projecteuclid.org/euclid.aihp/1395856131


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