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arXiv · 0805.0867

On the Eigenspaces of Lamplighter Random Walks and Percolation Clusters on Graphs

Franz Lehner
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Abstract

We show that the Plancherel measure of the lamplighter random walk on a graph coincides with the expected spectral measure of the absorbing random walk on the Bernoulli percolation clusters. In the subcritical regime the spectrum is pure point and we construct a complete orthonormal basis of finitely supported eigenfunctions.

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Franz Lehner. 2008-06-04. On the Eigenspaces of Lamplighter Random Walks and Percolation Clusters on Graphs. https://doi.org/10.1090/s0002-9939-09-09869-4

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