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.