Invariance principle for the random conductance model with dynamic bounded conductances

Sebastian Andres

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 2, page 352-374
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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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 50.2 (2014): 352-374. <http://eudml.org/doc/272014>.

@article{Andres2014,
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.},
author = {Andres, Sebastian},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random conductance model; dynamic environment; invariance principle; ergodic; corrector; point of view of the particle; stochastic interface model},
language = {eng},
number = {2},
pages = {352-374},
publisher = {Gauthier-Villars},
title = {Invariance principle for the random conductance model with dynamic bounded conductances},
url = {http://eudml.org/doc/272014},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Andres, Sebastian
TI - Invariance principle for the random conductance model with dynamic bounded conductances
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 2
SP - 352
EP - 374
AB - 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.
LA - eng
KW - random conductance model; dynamic environment; invariance principle; ergodic; corrector; point of view of the particle; stochastic interface model
UR - http://eudml.org/doc/272014
ER -

References

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