Spectral asymptotics of percolation Hamiltonians on amenable Cayley graphs

Details Spectral asymptotics of percolation Hamiltonians on amenable Cayley graphs Spectral asymptotics of percolation Hamiltonians on amenable Cayley graphs

2007-07-29

arxiv.org/abs/0707.4292v2

Operator Theory: Advances and Applications, Volume 186, pages, 1-29, 2008

Mathematics

Spectral Theory

Typos (including those found after publication)corrected

Scientific paper

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.

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