Recently, several papers have been devoted to the analysis of lamplighter random walks, in particular, in the case where the underlying graph is the infinite path Z. In the present paper, we develop a spectral analysis for lamplighter random walks on finite graphs. In the general case, we use the C-2-symmetry to reduce the spectral computations to a series of eigenvalue problems on the underlying graph. If the graph has a transitive isometry group G, we also describe the spectral analysis in terms of the representation theory of the wreath product C-2 (sic) G. We apply our theory to the lamplighter random walks on the complete graph and on the discrete circle. These examples have already been studied by Haggstrom and Jonasson by probabilistic methods.

Harmonic analysis of finite lamplighter random walks / Scarabotti, Fabio; Filippo, Tolli. - In: JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS. - ISSN 1079-2724. - STAMPA. - 14:2(2008), pp. 251-282. [10.1007/s10883-008-9038-8]

Harmonic analysis of finite lamplighter random walks

SCARABOTTI, Fabio;
2008

Abstract

Recently, several papers have been devoted to the analysis of lamplighter random walks, in particular, in the case where the underlying graph is the infinite path Z. In the present paper, we develop a spectral analysis for lamplighter random walks on finite graphs. In the general case, we use the C-2-symmetry to reduce the spectral computations to a series of eigenvalue problems on the underlying graph. If the graph has a transitive isometry group G, we also describe the spectral analysis in terms of the representation theory of the wreath product C-2 (sic) G. We apply our theory to the lamplighter random walks on the complete graph and on the discrete circle. These examples have already been studied by Haggstrom and Jonasson by probabilistic methods.
gelfand pair; harmonic analysis; lamplighter random walk; lamplighter random walks; markov spectrum; mixing time; permutation representation; wreath product
01 Pubblicazione su rivista::01a Articolo in rivista
Harmonic analysis of finite lamplighter random walks / Scarabotti, Fabio; Filippo, Tolli. - In: JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS. - ISSN 1079-2724. - STAMPA. - 14:2(2008), pp. 251-282. [10.1007/s10883-008-9038-8]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/71386
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