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The spectra of lamplighter groups and Cayley machines |
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| Authors: | Mark Kambites Pedro V Silva Benjamin Steinberg |
| Institution: | 1. Fachbereich Mathematik/Informatik, Universit?t Kassel, 34109, Kassel, Germany 2. Departamento de Matemática Pura, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal 3. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada |
| Abstract: | We calculate the spectra and spectral measures associated to random walks on restricted wreath products G wr  , 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. |
| Keywords: | Automata group Wreath product Markov operator Spectra Lamplighters Random walks |
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