Averaged large deviations for random walk in a random environment

Atilla Yilmaz

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 3, page 853-868
  • ISSN: 0246-0203

Abstract

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In his 2003 paper, Varadhan proves the averaged large deviation principle for the mean velocity of a particle taking a nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on ℤd with d≥1, and gives a variational formula for the corresponding rate function Ia. Under Sznitman’s transience condition (T), we show that Ia is strictly convex and analytic on a non-empty open set , and that the true velocity of the particle is an element (resp. in the boundary) of when the walk is non-nestling (resp. nestling). We then identify the unique minimizer of Varadhan’s variational formula at any velocity in .

How to cite

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Yilmaz, Atilla. "Averaged large deviations for random walk in a random environment." Annales de l'I.H.P. Probabilités et statistiques 46.3 (2010): 853-868. <http://eudml.org/doc/240145>.

@article{Yilmaz2010,
abstract = {In his 2003 paper, Varadhan proves the averaged large deviation principle for the mean velocity of a particle taking a nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on ℤd with d≥1, and gives a variational formula for the corresponding rate function Ia. Under Sznitman’s transience condition (T), we show that Ia is strictly convex and analytic on a non-empty open set , and that the true velocity of the particle is an element (resp. in the boundary) of when the walk is non-nestling (resp. nestling). We then identify the unique minimizer of Varadhan’s variational formula at any velocity in .},
author = {Yilmaz, Atilla},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {disordered media; rare events; rate function; regeneration times},
language = {eng},
number = {3},
pages = {853-868},
publisher = {Gauthier-Villars},
title = {Averaged large deviations for random walk in a random environment},
url = {http://eudml.org/doc/240145},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Yilmaz, Atilla
TI - Averaged large deviations for random walk in a random environment
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 3
SP - 853
EP - 868
AB - In his 2003 paper, Varadhan proves the averaged large deviation principle for the mean velocity of a particle taking a nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on ℤd with d≥1, and gives a variational formula for the corresponding rate function Ia. Under Sznitman’s transience condition (T), we show that Ia is strictly convex and analytic on a non-empty open set , and that the true velocity of the particle is an element (resp. in the boundary) of when the walk is non-nestling (resp. nestling). We then identify the unique minimizer of Varadhan’s variational formula at any velocity in .
LA - eng
KW - disordered media; rare events; rate function; regeneration times
UR - http://eudml.org/doc/240145
ER -

References

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