Work

Random Perturbations of Matrix Polynomials

Year: 2020

Type: article

Abstract: A sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial converges to some deterministic limit. A formula for the limit of the resolvent of the sum is derived, and the eigenvalues are localised. Four instances are considered: a low-rank matrix perturbed by the Wigner matrix, a product HX of a fixed diagonal matrix H and the Wigner matrix X and two special matrix polynomials of higher degree. The results are illustrated with various examples and numerical simulations.

Source: Journal of Theoretical Probability

DOI: 10.1007/s10959-020-01048-3

Authors: Patryk Pagacz, Michał Wojtylak

Institution: Jagiellonian University

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,750

Funder: Narodowe Centrum Nauki