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 $\mathcal{A}$ , and that the true velocity of the particle is an element (resp. in the boundary) of $\mathcal{A}$ when the walk is non-nestling (resp. nestling). We then identify the unique minimizer of Varadhan’s variational formula at any velocity in $\mathcal{A}$ .
@article{1281100401,
author = {Yilmaz, Atilla},
title = {Averaged large deviations for random walk in a random environment},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 853-868},
language = {en},
url = {http://dml.mathdoc.fr/item/1281100401}
}
Yilmaz, Atilla. Averaged large deviations for random walk in a random environment. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 853-868. http://gdmltest.u-ga.fr/item/1281100401/