Uniform Approximation of the Integrated Density of States for Long-Range Percolation Hamiltonians |
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Authors: | Fabian Schwarzenberger |
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Institution: | 1.Fakult?t für Mathematik,TU Chemnitz,Chemnitz,Germany |
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Abstract: | 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. |
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Keywords: | |
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