Harmonic analysis of finite lamplighter random walks

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dc.creatorScarabotti, Fabio
dc.creatorTolli, Filippo
dc.date2007-01-22
dc.date.accessioned2026-07-07T09:37:08Z
dc.date.available2026-07-07T09:37:08Z
dc.descriptionRecently, several papers have been devoted to the analysis of lamplighter random walks, in particular when the underlying graph is the infinite path $\mathbb{Z}$. 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. In the case the graph has a transitive isometry group $G$, we also describe the spectral analysis in terms of the representation theory of the wreath product $C_2\wr G$. We apply our theory to the lamplighter random walks on the complete graph and on the discrete circle. These examples were already studied by Haggstrom and Jonasson by probabilistic methods.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math/0701603
dc.identifierhttp://arxiv.org/abs/math/0701603
dc.identifierJ. Dynam. Control Systems 14 (2008), no. 2, 251--282.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160354
dc.subjectProbability
dc.subjectRepresentation Theory
dc.subjectPrimary: 43A85; secondary: 05C05, 20C15, 20E22, 60G50
dc.titleHarmonic analysis of finite lamplighter random walks
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