Felix Pogorzelski, Fabian Schwarzenberger, Christian Seifert:Uniform existence of the integrated density of states on metric Cayley graphs

Author(s):

Felix Pogorzelski
Fabian Schwarzenberger
Christian Seifert

Title:

Felix Pogorzelski, Fabian Schwarzenberger, Christian Seifert:Uniform existence of the integrated density of states on metric Cayley graphs

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 22, 2011

Mathematics Subject Classification:

47E05	[]
34L40	[]
47B80	[]
81Q10	[]

Abstract:

Given a finitely generated amenable group we consider ergodic random Schr\"odinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normalised eigenvalue counting functions of finite volume parts converge uniformly. The integrated density of states as the limit can be expressed by a Pastur-Shubin formula. The spectrum supports the corresponding measure and discontinuities correspond to the existence of compactly supported eigenfunctions.

Keywords:

random Schrödinger operator, metric graph, quantum graph, integrated density of states

Language:

English

Publication time:

12/2011