Precise large deviation estimates for a one-dimensional random walk in a random environment
成果类型：
Article
署名作者：
Pisztora, A; Povel, T; Zeitouni, O
署名单位：
Harvard University; Massachusetts Institute of Technology (MIT); Technion Israel Institute of Technology
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s004400050206
发表日期：
1999
页码：
191-219
关键词：
摘要：
Suppose that the integers are assigned i.i.d. random variables {w(x)} (taking values in the interval [1/2, 1)), which serve as an environment. This environment defines a random walk {X-k} (called a RWRE) which, when at x, moves one step to the right with probability omega(x), and one step to the left with probability 1 - omega(x). Solomon (1975) determined the almost-sure asymptotic speed (= rate of escape) of a RWRE, in a more general set-up. Dembo, Peres and Zeitouni (1996), following earlier work by Greven and den Hollander (1994) on the quenched case, have computed rough tail asymptotics for the empirical mean of the annealed RWRE. They conjectured the form of the rate function in a full LDP. We prove in this paper their conjecture. The proof is based on a coarse graining scheme together with comparison techniques.
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