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.
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I sincerely thank O. Zeitouni for many valuable discussions and comments.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Yilmaz, A. Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher. Probab. Theory Relat. Fields 149, 463–491 (2011). https://doi.org/10.1007/s00440-010-0261-3
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DOI: https://doi.org/10.1007/s00440-010-0261-3