Quenched large deviations for multidimensional random walk in random environment: a variational formula

2008/04/09 by Jeffrey M. Rosenbluth, Rosenbluth, Jeffrey M. · 3 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F10. #82C44 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0804.1444

openalex publication_date 2008/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 subadditive ergodic theorem. We employ a different technique which is based on a minimax 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.

Citations

• Foundations of Modern Probability

Cited by

• Limiting distributions and large deviations for random walks in random environments
• Large deviations for random walk in a random environment
• Quenched Large Deviations for Simple Random Walks on Supercritical\n Percolation Clusters

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