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), p. 352-374 / Harvested from Numdam

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Résumé
Abstract

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

Publié le : 2014-01-01

MR 3189075 | Zbl 1290.60109

DOI : https://doi.org/10.1214/12-AIHP527
Classification: 60K37, 60F17, 82C41

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     author = {Andres, Sebastian},
     title = {Invariance principle for the random conductance model with dynamic bounded conductances},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {50},
     year = {2014},
     pages = {352-374},
     doi = {10.1214/12-AIHP527},
     mrnumber = {3189075},
     zbl = {1290.60109},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2014__50_2_352_0}
}

Andres, Sebastian. Invariance principle for the random conductance model with dynamic bounded conductances. Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) pp. 352-374. doi : 10.1214/12-AIHP527. http://gdmltest.u-ga.fr/item/AIHPB_2014__50_2_352_0/

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