Uniform Approximation of the Integrated Density of States for Long-Range Percolation Hamiltonians

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. This re...

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Bibliographic Details
Published in:Journal of statistical physics 2012-03, Vol.146 (6), p.1156-1183
Main Author: Schwarzenberger, Fabian
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Toy industry
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Summary: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. This result is already new for percolation on ℤ d . Using this, we are able to characterize the set of discontinuities of the IDS.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-012-0431-z