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

被引：0
|
作者：
Fabian Schwarzenberger
机构：
[1] TU Chemnitz,Fakultät für Mathematik
来源：
Journal of Statistical Physics | 2012年 / 146卷
关键词：
Spectral theory; Long-range percolation; Integrated density of states; Uniform approximation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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 ℤd. Using this, we are able to characterize the set of discontinuities of the IDS.
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页码：1156 / 1183
页数：27
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