Title:

Lifshitz tail estimates on percolation graphs of polynomial growth

Tonći Antunović

Abstract:

We study discrete Laplace operators on subcritical percolation subgraphs of amenable Cayley graphs. The growth rate of the graph is reflected through the asymptotical behaviour of the integrated density of states. In particular, following the results of Kirsch and Müller in the lattice case, we prove the Lifshitz tail behaviour in the case of polynomial growth.