Work

Eigenvalue gaps of random perturbations of large matrices

Year: 2025

Type: article

Abstract: This work applies some recent combinatorial tools due to Jain to control the eigenvalue gaps of a matrix [Formula: see text] where [Formula: see text] is deterministic, symmetric with large operator norm and [Formula: see text] is a random symmetric matrix with sub-Gaussian entries. One consequence of our tail bounds is that [Formula: see text] has simple spectrum with probability at least [Formula: see text] which improves on a result of Nguyen, Tao and Vu in terms of both the probability and the size of the matrix [Formula: see text].

Source: Random Matrices Theory and Application

DOI: 10.1142/s2010326325500170

Authors: Kyle Luh, Ryan Vogel, Alan Yu

Institution: University of Colorado Boulder

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Simons Foundation

Award: G8622106442