Uniform approximation of the integrated density of states for long-range percolation Hamiltonians

Details Uniform approximation of the integrated density of states for long-range percolation Hamiltonians Uniform approximation of the integrated density of states for long-range percolation Hamiltonians

2010-11-18

arxiv.org/abs/1011.4192v1

Mathematics

Spectral Theory

Scientific paper

In this paper we study the spectrum of long-range percolation graphs. The
underlying geometry is given in terms of a finitely generated amenable group.
We prove that the integrated density of states (IDS) or spectral distribution
function can be approximated uniformly in the energy variable. Using this, we
are able to characterise the set of discontinuities of the IDS.

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