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.)