Averaged large deviations for random walk in a random environment

作者：Yilmaz Atilla^*

来源：Annales de l Institut Henri Poincare-Probabilites et Statistiques, 2010, 46(3): 853-868.

DOI：10.1214/09-AIHP332

• Disordered media
• Rare events
• Rate function
• Regeneration times

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 Z(d) with d >= 1, 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 A, and that the true velocity of the particle is an element (resp. in the boundary) of A when the walk is non-nestling (resp. nestling). We then identify the unique minimizer of Varadhan's variational formula at any velocity in A.

• 出版日期2010-8