Singularity degree of structured random matrices

Krüger T, Renfrew D (2025)

Publication Type: Journal article

Publication year: 2025

Journal

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

Book Volume: 61

Pages Range: 1416-1442

Journal Issue: 2

DOI: 10.1214/24-AIHP1464

Abstract

We consider the density of states of structured Hermitian random matrices with a variance profile. As the dimension tends to infinity the associated eigenvalue density can develop a singularity at the origin. The severity of this singularity depends on the relative positions of the zero submatrices. We provide a classification of all possible singularities and determine the exponent in the density blow-up, which we label the singularity degree.

Authors with CRIS profile

Torben Krüger Lehrstuhl für Mathematische Stochastik

Involved external institutions

Binghamton University / State University of New York, Binghamton US United States (USA) (US)

How to cite

APA:

Krüger, T., & Renfrew, D. (2025). Singularity degree of structured random matrices. Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques, 61(2), 1416-1442. https://doi.org/10.1214/24-AIHP1464

MLA:

Krüger, Torben, and David Renfrew. "Singularity degree of structured random matrices." Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques 61.2 (2025): 1416-1442.

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