QUENCHED LIMITS FOR TRANSIENT, ZERO SPEED ONE-DIMENSIONAL RANDOM WALK IN RANDOM ENVIRONMENT
成果类型：
Article
署名作者：
Peterson, Jonathon; Zeitouni, Ofer
署名单位：
University of Wisconsin System; University of Wisconsin Madison; University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/08-AOP399
发表日期：
2009
页码：
143-188
关键词：
摘要：
We consider it nearest-neighbor, one dimensional random walk (X-n)(n >= 0) in a random i.i.d. environment. in the regime where the walk is transient but with zero speed, so that X-n is of order n(s) for some s < 1. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible: There exist sequences {n(k)} and {x(k)} depending on the environment only, such that Xn(k) - x(k) = 0(logn(k))(2) (a localized regime). On the other hand, there exist sequences {t(m)} and {s(m)} depending on the environment only, such that log s(m)/log t(m) -> s < 1 and P-omega (X-tm/(sm)<= x) -> 1/2 for all x > 0 and -> 0 for x <= 0 (a spread out regime).