Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher

Abstract

We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment. It is easy to see that the quenched and the averaged rate functions are not identically equal. When the dimension is at least four and Sznitman's transience condition (T) is satisfied, we prove that these rate functions are finite and equal on a closed set whose interior contains every nonzero velocity at which the rate functions vanish.

17 pages. Minor revision. In particular, note the change in the title of the paper. To appear in Probability Theory and Related Fields.

References in corpus (3)

• Transient Random Walks in Random Environment on a Galton-Watson Tree
• Coincidence of Lyapunov exponents for random walks in weak random potentials
• Large deviations for random walk in a space--time product environment

Cited by in corpus (5)

• Differing averaged and quenched large deviations for random walks in random environments in dimensions two and three
• Diffusion in time-dependent random media and the Kardar-Parisi-Zhang equation
• A proof of Sznitman's conjecture about ballistic RWRE
• Harmonic functions, h-transform and large deviations for random walks in random environments in dimensions four and higher
• On large deviation rate functions for a continuous-time directed polymer in weak disorder