On the eigenspaces of lamplighter random walks and percolation clusters on graphs

Franz Lehner
2009 Proceedings of the American Mathematical Society  
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.
doi:10.1090/s0002-9939-09-09869-4 fatcat:oupizu63jrcqbkdkp4ov2mhda4