A monotonicity property for random walk in a partially random environment

Mark Holmes and Rongfeng Sun

Stochastic Processes and their Applications, 2012, vol. 122, issue 4, pages 1369-1396

Abstract: We prove a law of large numbers for random walks in certain kinds of i.i.d. random environments in Zd that is an extension of a result of Bolthausen et al. (2003) [4]. 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.

Keywords: Random walk in a random environment; Monotonicity of speed; Lace expansion (search for similar items in EconPapers)
Date: 2012
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