Work

Dynamics of an outlier in the Gaussian unitary ensemble

Year: 2025

Type: article

Abstract: We endow the elements of a random matrix drawn from the Gaussian unitary ensemble with a Dyson Brownian motion dynamics. We initialize the dynamics of the eigenvalues with all of them lumped at the origin, but one outlier. We solve the dynamics exactly, which gives us a window on the dynamical scaling behavior at and around the Baik-Ben Arous-Péché transition. Amusingly, while the statics is well known and accessible via the Hikami-Brézin integrals, our approach for the dynamics is explicitly based on the use of orthogonal polynomials.

Source: Physical review. E

DOI: 10.1103/22b9-4q39

Authors: John Mateus, Gabriel Téllez, Frédéric van Wijland

Institutions: Universidad de Los Andes, Centre National de la Recherche Scientifique, Université Paris Cité, Kyoto University, Laboratoire Matière et Systèmes Complexes

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Universidad de los Andes

Awards: G3171795598, G633440783