Averaged Large Deviations for Random Walk in a Random Environment
نویسنده
چکیده
Abstract. In his 2003 paper, Varadhan proves the averaged large deviation principle (LDP) for the mean velocity of a particle performing random walk in a random environment (RWRE) on Z with d ≥ 1, and gives a variational formula for the corresponding rate function Ia. Under the non-nestling assumption (resp. Kalikow’s condition), we show that Ia is strictly convex and analytic on a non-empty open set A, and that the true velocity ξo of the particle is an element (resp. in the closure) of A. We then identify the minimizer of Varadhan’s variational formula at any ξ ∈ A.
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