Random walks on the lamplighter group
成果类型：
Article
署名作者：
Lyons, R; Pemantle, R; Peres, Y
署名单位：
University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1996
页码：
1993-2006
关键词：
摘要：
Kaimanovich and Vershik described certain finitely generated groups of exponential growth such that simple random walk on their Cayley graph escapes from the identity at a sublinear rate, or equivalently, all bounded harmonic functions on the Cayley graph are constant. Here we focus on a key example, called G(1) by Kaimanovich and Vershik, and show that inward-biased random walks on G(1) move outward faster than simple random walk. Indeed, they escape from the identity at a linear rate provided that the bias parameter is smaller than the growth rate of G(1). These walks can be viewed as random walks interacting with a dynamical environment on Z. The proof uses potential theory to analyze a stationary environment as seen from the moving particle.