Lyapounov exponents and quenched large deviations for multidimensional random walk in random environment
成果类型：
Article
署名作者：
Zerner, MPW
署名单位：
Swiss Federal Institutes of Technology Domain; ETH Zurich
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1022855870
发表日期：
1998
页码：
1446-1476
关键词：
摘要：
Assign to the lattice sizes z is an element of Z(d) i.i.d. random 2d-dimensional vectors (omega(z, z + e))(/e/ = 1) whose entries take values in the open unit interval and add up to one. Given a realization w of this environment, let (X-n)(n greater than or equal to 0) be a Markov chain on hd which, when at z, moves one step to its neighbor z + e with transition probability omega(z, z + e). We derive a large deviation principle for X-n/n by means of a result similar to the shape theorem of first-passage percolation and related models. This result produces certain constants that are the analogue of the Lyapounov exponents known from Brownian motion in Poissonian potential or random walk in random potential. We follow a strategy similar to Sznitman.