Einstein relation for reversible diffusions in a random environment | Zendy

Gantert Nina | Zendy; Mathieu Pierre | Zendy; Piatnitski Andrey | Zendy

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Einstein relation for reversible diffusions in a random environment

Author(s) -

Gantert Nina,

Mathieu Pierre,

Piatnitski Andrey

Publication year - 2012

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.20389

Subject(s) - einstein relation , einstein , girsanov theorem , mathematics , relation (database) , thermal diffusivity , statistical physics , variety (cybernetics) , random walk , homogenization (climate) , pure mathematics , mathematical physics , computer science , statistics , thermodynamics , physics , data mining , biodiversity , ecology , metric (unit) , operations management , stochastic differential equation , biology , economics

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. © 2011 Wiley Periodicals, Inc.

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