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

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.

notational improvements and minor corrections, 6 pages; complement to arXiv:0712.3135

References in corpus (1)

• On the spectrum of lamplighter groups and percolation clusters

Cited by in corpus (1)

• Free Lamplighter Groups and a Question of Atiyah