The quenched invariance principle for random walks in random environments admitting a bounded cycle representation

Jean-Dominique Deuschel; Holger Kösters

Annales de l'I.H.P. Probabilités et statistiques (2008)

  • Volume: 44, Issue: 3, page 574-591
  • ISSN: 0246-0203

Abstract

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We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman (Probab. Theory Related Fields129 (2004) 219–244) to the non-reversible setting.

How to cite

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Deuschel, Jean-Dominique, and Kösters, Holger. "The quenched invariance principle for random walks in random environments admitting a bounded cycle representation." Annales de l'I.H.P. Probabilités et statistiques 44.3 (2008): 574-591. <http://eudml.org/doc/77983>.

@article{Deuschel2008,
abstract = {We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman (Probab. Theory Related Fields129 (2004) 219–244) to the non-reversible setting.},
author = {Deuschel, Jean-Dominique, Kösters, Holger},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {invariance principle; random walks in random environments; non-reversible Markov chains; cycle representations},
language = {eng},
number = {3},
pages = {574-591},
publisher = {Gauthier-Villars},
title = {The quenched invariance principle for random walks in random environments admitting a bounded cycle representation},
url = {http://eudml.org/doc/77983},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Deuschel, Jean-Dominique
AU - Kösters, Holger
TI - The quenched invariance principle for random walks in random environments admitting a bounded cycle representation
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2008
PB - Gauthier-Villars
VL - 44
IS - 3
SP - 574
EP - 591
AB - We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman (Probab. Theory Related Fields129 (2004) 219–244) to the non-reversible setting.
LA - eng
KW - invariance principle; random walks in random environments; non-reversible Markov chains; cycle representations
UR - http://eudml.org/doc/77983
ER -

References

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  13. [13] P. Mathieu and A. Piatnitski. Quenched invariance principles for random walks on percolation clusters. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 463 (2007) 2287–2307. Zbl1131.82012MR2345229
  14. [14] V. Sidoravicius and A.-S. Sznitman. Quenched invariance principles for walks on clusters of percolation or among random conductances. Probab. Theory Related Fields 129 (2004) 219–244. Zbl1070.60090MR2063376
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