Statistics Seminars: Asymptotic behavior of the integrated density of states of percolation Laplacians
16 February 2007 15:15 in CM221
The integrated density of states (IDS) is a well defined notion for discrete Laplace operators on Cayley graphs of finitely generated amenable groups. In the talk we will restrict ourselves to the subcritical percolation case, where the Laplacian is a random operator defined on subcritical percolation subgraphs. We are interested in the asymptotic behavior of the IDS while approaching the lower spectral edge. This behavior depends on the growth rate of the graph. In particular there is a dependency on whether the growth is polynomial or superpolynomial. The results are obtained following the arguments of Werner Kirsch and Peter Müller in the lattice case and using the isoperimetric inequality of Coulhon & Saloff-Coste.
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