A monotonicity property for random walk in a partially random environment

作者：Holmes Mark; Sun Rongfeng^*

来源：Stochastic Processes and Their Applications, 2012, 122(4): 1369-1396.

DOI：10.1016/j.spa.2012.01.006

• Random walk in a random environment
• Monotonicity of speed
• Lace expansion

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 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.

• 出版日期2012-4