On the disconnection of a discrete cylinder by a biased random walk
成果类型：
Article
署名作者：
Windisch, David
署名单位：
Swiss Federal Institutes of Technology Domain; ETH Zurich
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/07-AAP491
发表日期：
2008
页码：
1441-1490
关键词：
摘要：
We consider a random walk on the discrete cylinder (7G/NZ)d x 7G, d >_ 3 with drift N-d,, in the 7G-direction and investigate the large N-behavior of the disconnection time TNts, defined as the first time when the trajectory of the random walk disconnects the cylinder into two infinite components. We prove that, as long as the drift exponent a is strictly greater than 1, the asymptotic behavior of TNts remains NZd+o(1) as in the unbiased case considered by Dembo and Sznitman, whereas for a < 1, the asymptotic behavior of Tntsc becomes exponential in N.