Oscillation Theory for the Density of States of High Dimensional Random Operators

Publikationstyp
Journal Article
Date Issued
2019-08-01
Sprache
English
Author(s)
Großmann, Julian Peter  orcid-logo
Schulz-Baldes, Hermann  
Villegas-Blas, Carlos  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/6016
Journal
International mathematics research notices  
Volume
2019
Issue
15
Start Page
4579
End Page
4602
Citation
International Mathematics Research Notices 15 (2019): 4579-4602 (2019-08-01)
Publisher DOI
10.1093/imrn/rnx246
Scopus ID
2-s2.0-85083892239
Sturm-Liouville oscillation theory is studied for Jacobi operators with block entries given by covariant operators on an infinite dimensional Hilbert space. It is shown that the integrated density of states of the Jacobi operator is approximated by the winding of the Prüfer phase w.r.t. the trace per unit volume. This rotation number can be interpreted as a spectral flow in a von Neumann algebra with finite trace.