Oscillation Theory for the Density of States of High Dimensional Random Operators-Reference-Cited by-同舟云学术

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

Published:2017-10-12 Issue:15 Volume:2019 Page:4579-4602
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Groß mann Julian¹²,Schulz-Baldes Hermann¹³,Villegas-Blas Carlos³⁴

Affiliation:

1. Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, D-91058 Erlangen, Germany

2. Institut für Mathematik, Technische Universität Hamburg, Am Schwarzenberg-Campus 3, D-21073 Hamburg, Germany

3. Instituto de Matemáticas, UNAM, Unidad Cuernavaca, Av. Universidad, Código Postal 62210, Cuernavaca, Morelos, Mexico

4. Laboratorio Solomon Lefschetz, Unidad Mixta Internacional del CNRS, Cuernavaca, Av. Universidad, Código Postal 62210, Cuernavaca, Morelos, Mexico

Abstract

Abstract 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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2019/15/4579/29028446/rnx246.pdf

Reference16 articles.

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