Journal
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
Volume 65, Issue 2, Pages 187-228Publisher
WILEY-BLACKWELL
DOI: 10.1002/cpa.20389
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We consider reversible diffusions in a random environment and prove the Einstein relation for this model. It says that the derivative at 0 of the effective velocity under an additional local drift equals the diffusivity of the model without drift. The Einstein relation is conjectured to hold for a variety of models but so far it has only been proved in particular cases. Our proof makes use of homogenization arguments, the Girsanov transform, and a refinement of the regeneration times introduced by Shen. (C) 2011 Wiley Periodicals, Inc.
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