Location of the spectrum of Kronecker random matrices

Alt J, Erdos L, Krueger T, Nemish Y (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques Elsevier Masson / Institute Henri Poincaré

Book Volume: 55

Pages Range: 661-696

Journal Issue: 2

DOI: 10.1214/18-AIHP894

Abstract

For a general class of large non-Hermitian random block matrices X we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained from the Dyson equation of the Hermitization of X as the self-consistent approximation of the pseudospectrum. We demonstrate that the analysis of the matrix Dyson equation from (Probab. Theory Related Fields (2018)) offers a unified treatment of many structured matrix ensembles.

Authors with CRIS profile

Torben Krüger

Involved external institutions

IST Austria AT Austria (AT) Rheinische Friedrich-Wilhelms-Universität Bonn DE Germany (DE)

How to cite

APA:

Alt, J., Erdos, L., Krueger, T., & Nemish, Y. (2019). Location of the spectrum of Kronecker random matrices. Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques, 55(2), 661-696. https://doi.org/10.1214/18-AIHP894

MLA:

Alt, Johannes, et al. "Location of the spectrum of Kronecker random matrices." Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques 55.2 (2019): 661-696.

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