Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel–Leader graphs |
| |
Authors: | Sara Brofferio Wolfgang Woess |
| |
Affiliation: | Institut für Mathematik C, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria |
| |
Abstract: | We determine the precise asymptotic behaviour (in space) of the Green kernel of simple random walk with drift on the Diestel–Leader graph , where q,r2. The latter is the horocyclic product of two homogeneous trees with respective degrees q+1 and r+1. When q=r, it is the Cayley graph of the wreath product (lamplighter group) with respect to a natural set of generators. We describe the full Martin compactification of these random walks on -graphs and, in particular, lamplighter groups. This completes previous results of Woess, who has determined all minimal positive harmonic functions. |
| |
Keywords: | Lamplighter group Wreath product Diestel– Leader graph Random walk Martin boundary Harmonic functions |
本文献已被 ScienceDirect 等数据库收录! |
|