A monotonicity property for random walk in a partially random environment

2010/05/06 by Mark Holmes, Holmes, Mark, Rongfeng Sun +1
Decision Sciences · Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1005.0927

openalex publication_date 2010/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a law of large numbers for random walks in certain kinds of i.i.d. random environments in Z^d that is an extension of a result of Bolthausen, Sznitman and Zeitouni (2003). We use this result, along with the lace expansion for self-interacting random walks, to prove a monotonicity result for the first coordinate of the speed of the random walk under some strong assumptions on the distribution of the environment.

Citations

• A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high\n biases

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