Einstein relation for reversible diffusions in a random environment

被引：22

作者：

Gantert, Nina ^{[1
]}

Mathieu, Pierre ^{[4
]}

Piatnitski, Andrey ^{[2
,3
]}

机构：

[1] Tech Univ Munich, Fak Math, D-85748 Garching, Germany

[2] Narvik Univ Coll, Narvik, Norway

[3] Russian Acad Sci, PN Lebedev Phys Inst, Moscow 119991, Russia

[4] Univ Aix Marseille 1, Ctr Math & Informat, F-13013 Marseille, France

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2012年 / 65卷 / 02期

关键词：

MARKOV-PROCESSES; RANDOM-WALK; INVARIANCE-PRINCIPLE; MOTT LAW; HOMOGENIZATION; PARTICLE;

D O I：

10.1002/cpa.20389

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：187 / 228

页数：42

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