Large deviations for disordered bosons and multiple orthogonal polynomial ensembles

TL;DR

This paper establishes a large deviations principle for empirical measures in various complex polynomial ensembles, including models relevant to disordered bosons and Chern-Simons theory, advancing understanding of their probabilistic behavior.

Contribution

It introduces a unified large deviations framework applicable to multiple orthogonal polynomial ensembles and related matrix models, including disordered bosons.

Findings

Proves a large deviations principle for these ensembles.

Includes models like biorthogonal Laguerre, Jacobi, Hermite, and others.

Provides insights into the probabilistic structure of complex matrix models.

Abstract

We prove a large deviations principle for the empirical measures of a class of biorthogonal and multiple orthogonal polynomial ensembles that includes biorthogonal Laguerre, Jacobi and Hermite ensembles, the matrix model of Lueck, Sommers and Zirnbauer for disordered bosons, the Stieltjes-Wigert matrix model of Chern-Simons theory, and Angelesco ensembles.