Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher
Probability
2010-04-09 v2
Abstract
We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment. It is easy to see that the quenched and the averaged rate functions are not identically equal. When the dimension is at least four and Sznitman's transience condition (T) is satisfied, we prove that these rate functions are finite and equal on a closed set whose interior contains every nonzero velocity at which the rate functions vanish.
Keywords
Cite
@article{arxiv.0903.0410,
title = {Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher},
author = {Atilla Yilmaz},
journal= {arXiv preprint arXiv:0903.0410},
year = {2010}
}
Comments
17 pages. Minor revision. In particular, note the change in the title of the paper. To appear in Probability Theory and Related Fields.