Publisher DOI: 10.1007/s11005-013-0626-5
Title: Uniform existence of the integrated density of states on metric Cayley graphs
Language: English
Authors: Pogorzelski, Felix 
Schwarzenberger, Fabian 
Seifert, Christian  
Keywords: integrated density of states;metric graph;quantum graph;random Schrödinger operator
Issue Date: 19-Apr-2013
Publisher: Springer Science + Business Media B.V.
Source: Letters in Mathematical Physics 103 (9): 1009-1028 (2013)
Abstract (english): 
Given an arbitrary, finitely generated, amenable group we consider ergodic Schrödinger operators on a metric 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 (IDS) 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. In this context, the present work generalises the hitherto known uniform IDS approximation results for operators on the d-dimensional metric lattice to a very large class of geometries. © 2013 Springer Science+Business Media Dordrecht.
ISSN: 1573-0530
Institute: Mathematik E-10 
Document Type: Article
Journal: Letters in mathematical physics 
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