Norm convergence rate for multivariate quadratic polynomials of Wigner matrices

Fronk J, Krüger T, Nemish Y (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Journal of Functional Analysis Elsevier

Book Volume: 287

Article Number: 110647

Journal Issue: 12

DOI: 10.1016/j.jfa.2024.110647

Abstract

We study Hermitian non-commutative quadratic polynomials of multiple independent Wigner matrices. We prove that, with the exception of some specific reducible cases, the limiting spectral density of the polynomials always has a square root growth at its edges and prove an optimal local law around these edges. Combining these two results, we establish that, as the dimension N of the matrices grows to infinity, the operator norm of such polynomials q converges to a deterministic limit with a rate of convergence of N−2/3+o(1). Here, the exponent in the rate of convergence is optimal. For the specific reducible cases, we also provide a classification of all possible edge behaviors.

Involved external institutions

University of Copenhagen DK Denmark (DK) University of California, San Diego US United States (USA) (US)

How to cite

APA:

Fronk, J., Krüger, T., & Nemish, Y. (2024). Norm convergence rate for multivariate quadratic polynomials of Wigner matrices. Journal of Functional Analysis, 287(12). https://doi.org/10.1016/j.jfa.2024.110647

MLA:

Fronk, Jacob, Torben Krüger, and Yuriy Nemish. "Norm convergence rate for multivariate quadratic polynomials of Wigner matrices." Journal of Functional Analysis 287.12 (2024).

BibTeX: Download