Ivan Veselic (Chemnitz):

Percolation clusters on Cayley graphs and their spectra

ABSTRACT:

We discuss geometric properties of percolation clusters of the lattice Z^d and of general Cayley graphs. Thereafter we turn to spectral properties of Laplacians on the full Cayley graph and on percolation sub-graphs. The considered properties are encoded in the spectral distribution function. In particular, we discuss approximability by finite volume eigenvalue counting functions, and the asymptotic behaviour at low energies.