Uniform existence of the integrated density of states on metric Cayley graphs

Publikationstyp
Journal Article
Date Issued
2013-04-19
Sprache
English
Author(s)
Pogorzelski, Felix  
Schwarzenberger, Fabian  
Seifert, Christian  orcid-logo
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/11155
Journal
Letters in mathematical physics  
Volume
103
Issue
9
Start Page
1009
End Page
1028
Citation
Letters in Mathematical Physics 103 (9): 1009-1028 (2013)
Publisher DOI
10.1007/s11005-013-0626-5
Scopus ID
2-s2.0-84880513431
Publisher
Springer Science + Business Media B.V.
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.
Subjects
integrated density of states
metric graph
quantum graph
random Schrödinger operator
DDC Class
510: Mathematik