Averaged large deviations for random walk in a random environment

Details Averaged large deviations for random walk in a random environment Averaged large deviations for random walk in a random environment

2008-09-19

arxiv.org/abs/0809.3467v2

Mathematics

Probability

14 pages. In this revised version, I state and prove all of the results under Sznitman's (T) condition instead of Kalikow's co

Scientific paper

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 $\mathbb{Z}^d$ with $d\geq1$, and gives a variational formula for the corresponding rate function $I_a$. Under Sznitman's transience condition (T), we show that $I_a$ 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 $\mathcal{A}$.

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