Spectral properties of a class of random walks on locally finite groups

被引：4

作者：

Bendikov, Alexander ^{[1
]}

Bobikau, Barbara ^{[1
]}

Pittet, Christophe ^{[2
]}

机构：

[1] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland

[2] Aix Marseille Univ, I2M, F-13453 Marseille 13, France

来源：

GROUPS GEOMETRY AND DYNAMICS | 2013年 / 7卷 / 04期

关键词：

Random walk; locally finite group; ultra-metric space; infinite divisible distribution; Laplace transform; Kohlbecker transform; Legendre transform; return probability; spectral distribution; isospectral profile; ULTRACONTRACTIVITY; TRANSIENCE; RECURRENCE; PROFILE;

D O I：

10.4171/GGD/206

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study some spectral properties of random walks on infinite countable amenable groups with an emphasis on locally finite groups, e. g. the infinite symmetric group S-infinity. On locally finite groups, the random walks under consideration are driven by infinite divisible distributions. This allows us to embed our random walks into continuous time Levy processes. We obtain examples of fast/slow decays of return probabilities, a recurrence criterion, exact values and estimates of isospectral profiles and spectral distributions.

引用

页码：791 / 820

页数：30