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 $ \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. 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?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.
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