The Spectra of Lamplighter Groups and Cayley Machines
Group Theory
2007-05-23 v2 Spectral Theory
Abstract
We calculate the spectra and spectral measures associated to random walks on restricted wreath products of finite groups with the infinite cyclic group, by calculating the Kesten-von Neumann-Serre spectral measures for the random walks on Schreier graphs of certain groups generated by automata. This generalises the work of Grigorchuk and Zuk on the lamplighter group. In the process we characterise when the usual spectral measure for a group generated by automata coincides with the Kesten-von Neumann-Serre spectral measure.
Cite
@article{arxiv.math/0412412,
title = {The Spectra of Lamplighter Groups and Cayley Machines},
author = {Mark Kambites and Pedro V. Silva and Benjamin Steinberg},
journal= {arXiv preprint arXiv:math/0412412},
year = {2007}
}
Comments
36 pages, improved exposition, main results slightly strengthened