Quenched large deviation for multidimensional random walk in random environment: A variational formula |
Posted on:2007-07-09 | Degree:Ph.D | Type:Dissertation |
University:New York University | Candidate:Rosenbluth, Jeffrey M | Full Text:PDF |
GTID:1440390005479726 | Subject:Mathematics |
Abstract/Summary: | |
We take the point of view of the particle in a multidimensional nearest neighbor random walk in random environment (RWRE). We prove a quenched large deviation principle and derive a variational formula for the quenched rate function. Most of the previous results in this area rely on the subbadditive ergodic theorem. We employ a different technique which is based on a mini-max theorem. Large deviation principles for RWRE have been proven for i.i.d. nestling environments subject to a moment condition and for ergodic uniformly elliptic environments. We assume only that the environment is ergodic and the transition probabilities satisfy a moment condition. |
Keywords/Search Tags: | Environment, Random, Large deviation, Quenched |
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