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Oscillation Theory for the Density of States of High Dimensional Random Operators
Publikationstyp
Journal Article
Publikationsdatum
2019-08-01
Sprache
English
Institut
TORE-URI
Enthalten in
Volume
2019
Issue
15
Start Page
4579
End Page
4602
Citation
International Mathematics Research Notices 15 (2019): 4579-4602 (2019-08-01)
Publisher DOI
Scopus ID
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.