Oscillation theory for the density of states of high dimensional random operators

Großmann J, Schulz-Baldes H, Villegas-Blas C (2017)

Publication Language: English

Publication Type: Journal article

Future Publication Type: Journal article

Publication year: 2017

Journal

International Mathematics Research Notices Oxford University Press (OUP): Policy H - Oxford Open Option A

Book Volume: 2019

Pages Range: 4579–4602

Journal Issue: 15

DOI: 10.1093/imrn/rnx246

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 Pruefer 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.

Authors with CRIS profile

Julian Großmann Lehrstuhl für Darstellungstheorie Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

National Autonomous University of Mexico / Universidad Nacional Autónoma de México (UNAM) MX Mexico (MX)

How to cite

APA:

Großmann, J., Schulz-Baldes, H., & Villegas-Blas, C. (2017). Oscillation theory for the density of states of high dimensional random operators. International Mathematics Research Notices, 2019(15), 4579–4602. https://doi.org/10.1093/imrn/rnx246

MLA:

Großmann, Julian, Hermann Schulz-Baldes, and Carlos Villegas-Blas. "Oscillation theory for the density of states of high dimensional random operators." International Mathematics Research Notices 2019.15 (2017): 4579–4602.

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