Variance decay for functionals of the environment viewed by the particle

Jean-Christophe Mourrat

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 1, page 294-327
  • ISSN: 0246-0203

Abstract

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For the random walk among random conductances, we prove that the environment viewed by the particle converges to equilibrium polynomially fast in the variance sense, our main hypothesis being that the conductances are bounded away from zero. The basis of our method is the establishment of a Nash inequality, followed either by a comparison with the simple random walk or by a more direct analysis based on a martingale decomposition. As an example of application, we show that under certain conditions, our results imply an estimate of the speed of convergence of the mean square displacement of the walk towards its limit.

How to cite

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Mourrat, Jean-Christophe. "Variance decay for functionals of the environment viewed by the particle." Annales de l'I.H.P. Probabilités et statistiques 47.1 (2011): 294-327. <http://eudml.org/doc/244024>.

@article{Mourrat2011,
abstract = {For the random walk among random conductances, we prove that the environment viewed by the particle converges to equilibrium polynomially fast in the variance sense, our main hypothesis being that the conductances are bounded away from zero. The basis of our method is the establishment of a Nash inequality, followed either by a comparison with the simple random walk or by a more direct analysis based on a martingale decomposition. As an example of application, we show that under certain conditions, our results imply an estimate of the speed of convergence of the mean square displacement of the walk towards its limit.},
author = {Mourrat, Jean-Christophe},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {algebraic convergence to equilibrium; random walk in random environment; environment viewed by the particle; homogenization},
language = {eng},
number = {1},
pages = {294-327},
publisher = {Gauthier-Villars},
title = {Variance decay for functionals of the environment viewed by the particle},
url = {http://eudml.org/doc/244024},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Mourrat, Jean-Christophe
TI - Variance decay for functionals of the environment viewed by the particle
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 1
SP - 294
EP - 327
AB - For the random walk among random conductances, we prove that the environment viewed by the particle converges to equilibrium polynomially fast in the variance sense, our main hypothesis being that the conductances are bounded away from zero. The basis of our method is the establishment of a Nash inequality, followed either by a comparison with the simple random walk or by a more direct analysis based on a martingale decomposition. As an example of application, we show that under certain conditions, our results imply an estimate of the speed of convergence of the mean square displacement of the walk towards its limit.
LA - eng
KW - algebraic convergence to equilibrium; random walk in random environment; environment viewed by the particle; homogenization
UR - http://eudml.org/doc/244024
ER -

References

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