Multiple orthogonal polynomial ensembles

Details Multiple orthogonal polynomial ensembles Multiple orthogonal polynomial ensembles

2009-02-06

arxiv.org/abs/0902.1058v1

Contemporary Mathematics 507 (2010), 155--176

Mathematics

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20 pages, no figures

Scientific paper

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.

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