ON THE EIGENSPACES OF LAMPLIGHTER RANDOM WALKS AND PERCOLATION CLUSTERS ON GRAPHS

被引：2

作者：

Lehner, Franz ^{[1
]}

机构：

[1] Inst Math Strukturtheorie, A-8010 Graz, Austria

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 08期

关键词：

Wreath product; percolation; random walk; spectral measure; point spectrum; eigenfunctions;

D O I：

10.1090/S0002-9939-09-09869-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the Plancherel measure of the lamplighter random walk on a graph coincides with the expected spectral measure of the absorbing random walk on the Bernoulli percolation clusters. In the subcritical regime the spectrum is pure point and we construct a complete orthonormal basis consisting of finitely supported eigenfunctions.

引用

页码：2631 / 2637

页数：7

共 3 条

[1] Speetral computations on lamplighter groups and Diestel-Leader graphs [J].