The spectra of lamplighter groups and Cayley machines

Kambites, Mark and Silva, Pedro V. and Steinberg, Benjamin (2006) The spectra of lamplighter groups and Cayley machines. Geometria Dedicata, 120 (1). pp. 193-227. ISSN 0046-5755

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We calculate the spectra and spectral measures associated to random walks on restricted wreath products G wr $$\mathbb{Z}$$, 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 Żuk 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.

Item Type: Article
Uncontrolled Keywords: Automata group - Wreath product - Markov operator - Spectra - Lamplighters - Random walks
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User: Ms Lucy van Russelt
Date Deposited: 27 Mar 2007
Last Modified: 20 Oct 2017 14:12

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