In this paper we study spectral properties of adjacency and Laplace operators on percolation subgraphs of Cayley graphs of
amenable, finitely generated groups. In particular we describe the asymptotic behaviour of the integrated density of states
(spectral distribution function) of these random Hamiltonians near the spectral minimum.
The first part of the note discusses various aspects of the quantum percolation model, subsequently we formulate a series
of new results, and finally we outline the strategy used to prove our main theorem.
Keywords Amenable groups - Cayley graphs - random graphs - percolation - random operators - spectral graph theory - phase transition
Mathematics Subject Classification (2000) 05C25 - 82B43 - 05C80 - 37A30 - 35P15