Multiple orthogonal polynomial ensembles
Probability
2010-07-30 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.0902.1058,
title = {Multiple orthogonal polynomial ensembles},
author = {Arno B. J. Kuijlaars},
journal= {arXiv preprint arXiv:0902.1058},
year = {2010}
}
Comments
20 pages, no figures