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

Journal article


Publication Details

Author(s): Großmann J, Schulz-Baldes H, Villegas-Blas C
Journal: International Mathematics Research Notices
Publication year: 2017
ISSN: 1073-7928
Language: English


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.


FAU Authors / FAU Editors

Großmann, Julian
Lehrstuhl für Mathematik (Mathematische Physik)
Schulz-Baldes, Hermann Prof. Dr.
Professur für Mathematik (Mathematische Physik)


External institutions with authors

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


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. https://dx.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 (2017).

BibTeX: 

Last updated on 2019-22-07 at 07:33