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

Author(s):

Fabian Schwarzenberger

Title:

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

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 21, 2011

Mathematics Subject Classification:

22D40	[]
58C40	[]
81Q10	[]
82B43	[]

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. Using this, we are able to characterize the set of discontinuities of the IDS.

Keywords:

integrated density of states, uniform approximation, long-range percolation

Language:

English

Publication time:

12/2011