Ergodic and spectral properties of random colourings of graphs

Consider bond-percolation subgraphs of the Penrose tiling. We analyse spectral properties of the Laplacian on such graphs. Our results are valid in a more general framework, including graphs with a Delone vertex set. This extends investigations by Kirsch and Mueller (2006) for the hypercubic lattice case and by Hof (1998) for percolation on Penrose tilings.
(Joint work with Peter Müller.)