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25 April 2024

» arxiv » 0903.0410

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On the equality of the quenched and averaged large deviation rate functions for high-dimensional ballistic random walk in a random environment
Atilla Yilmaz ;
Date:	3 Mar 2009
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 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.
Source:	arXiv, 0903.0410
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