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

共 28 条

[21] Homogenization of divergence-form operators with lower-order terms in random media [J].

Lejay, A .

PROBABILITY THEORY AND RELATED FIELDS, 2001, 120 (02) :255-276

[22] Einstein relation for a tagged particle in simple exclusion processes [J].

Loulakis, M .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2002, 229 (02) :347-367

[23]

OSADA H, 1983, LECT NOTES MATH, V1021, P507

[24]

Papanicolaou G., 1982, Statistics and Probability, P547

[25]

Shen L, 2003, ANN I H POINCARE-PR, V39, P839, DOI [10.1016/S0246-0203(03)00027-X, 10.1016/S0246-0203(03)00027-X/FLA]

[26] An invariance principle for isotropic diffusions in random environment [J].

Sznitman, AS ;

Zeitouni, O .

INVENTIONES MATHEMATICAE, 2006, 164 (03) :455-567

[27] On the anisotropic walk on the supercritical percolation cluster [J].

Sznitman, AS .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 240 (1-2) :123-148

[28] A law of large numbers for random walks in random environment [J].

Sznitman, AS ;

Zerner, MPW .

ANNALS OF PROBABILITY, 1999, 27 (04) :1851-1869

← 1 2 3 →