Journal article
The spectra of lamplighter groups and Cayley machines
Publication Details
Authors: | Kambites, M.; Silva, P.; Steinberg, B. |
Publication year: | 2006 |
Journal: | Geometriae Dedicata |
Pages range : | 193-227 |
Volume number: | 120 |
Start page: | 193 |
End page: | 227 |
ISSN: | 0046-5755 |
eISSN: | 1572-9168 |
DOI-Link der Erstveröffentlichung: |
Abstract
We calculate the spectra and spectral measures associated to random walks on restricted wreath products G wr Z, with G a finite 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 an automaton coincides with the Kesten-von Neumann-Serre spectral measure.
We calculate the spectra and spectral measures associated to random walks on restricted wreath products G wr Z, with G a finite 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 an automaton coincides with the Kesten-von Neumann-Serre spectral measure.
