The spectra of lamplighter groups and Cayley machines

• Type: Article in International Scientific Journal
• Date: 2006

Authors

Kambites, M (Author) Other; Pedro V. Silva (Author) FCUP; Steinberg, B (Author) Other

Journal

Title: Geometriae Dedicata

Vol. 120 No. 1

Pages: 193-227

ISSN: 0046-5755

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 22 Citations

Scopus - 17 Citations

Other information

Authenticus ID: P-004-KDS

DOI: 10.1007/s10711-006-9086-8

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 35