The Einstein relation for random walks on graphs

被引：12

作者：

Teles, A ^{[1
]}

机构：

[1] Univ Technol & Econ Budapest, Dept Comp Sci & Informat Theory, H-1111 Budapest, Hungary

来源：

JOURNAL OF STATISTICAL PHYSICS | 2006年 / 122卷 / 04期

关键词：

exit times; random walks; Green's functions; Harnack inequality;

D O I：

10.1007/s10955-005-8002-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper investigates the Einstein relation; the connection between the volume growth, the resistance growth and the expected time a random walk needs to leave a ball on a weighted graph. The Einstein relation is proved under different set of conditions. In the simplest case it is shown under the volume doubling and time comparison principles. This and the other set of conditions provide the basic framework for the study of (sub-) diffusive behavior of the random walks on weighted graphs.

引用

页码：617 / 645

页数：29

共 18 条

[1]

ALEXANDER S, 1982, J PHYS LETT-PARIS, V43, pL625, DOI 10.1051/jphyslet:019820043017062500

[2]

[Anonymous], ANN PHYS

[3]

Barlow MT, 2004, REV MAT IBEROAM, V20, P1

[4] Stability of parabolic Harnack inequalities [J].

Barlow, MT ;

Bass, RF .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (04) :1501-1533

[5]

BARLOW MT, IN PRESS B LONDON MA

[6] History and heterogeneity, part 1 - Editor's introduction [J].

Barlow, TE .

POSITIONS-EAST ASIA CULTURES CRITIQUE, 1998, 6 (01) :1-6

[7] Random walks on graphs with regular volume growth [J].

Coulhon, T ;

Grigoryan, A .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 1998, 8 (04) :656-701

[8] Harnack inequalities and sub-Gaussian estimates for random walks [J].

Grigor'yan, A ;

Telcs, A .

MATHEMATISCHE ANNALEN, 2002, 324 (03) :521-556

[9] Sub-Gaussian estimates of heat kernels on infinite graphs [J].

Grigor'yan, A ;

Telcs, A .

DUKE MATHEMATICAL JOURNAL, 2001, 109 (03) :451-510

[10]

Hambly BM, 2004, P SYMP PURE MATH, V72, P233

← 1 2 →