Multiple orthogonal polynomial ensembles

TL;DR

This paper introduces multiple orthogonal polynomial ensembles (MOP ensembles), exploring their properties and connections to Angelesco and Nikishin systems within random matrix theory and equilibrium problems.

Contribution

It defines MOP ensembles and demonstrates their relation to Angelesco and Nikishin systems, expanding the understanding of their role in random matrix models.

Findings

MOP ensembles are linked to Angelesco and Nikishin systems.

Equilibrium problems are naturally interpreted within MOP ensembles.

Basic properties of MOP ensembles are derived.

Abstract

Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in random matrix theory. In this paper we introduce the notion of a multiple orthogonal polynomial ensemble (MOP ensemble) and derive some of their basic properties. It is shown that Angelesco and Nikishin systems give rise to MOP ensembles and that the equilibrium problems that are associated with these systems have a natural interpretation in the context of MOP ensembles.