This article is cited in 8 papers

A Vector Equilibrium Problem for Muttalib–Borodin Biorthogonal Ensembles

Arno B. J. Kuijlaars

Katholieke Universiteit Leuven, Department of Mathematics, Celestijnenlaan 200B box 2400, BE-3001 Leuven, Belgium

Abstract: The Muttalib–Borodin biorthogonal ensemble is a joint density function for $n$ particles on the positive real line that depends on a parameter $\theta$. There is an equilibrium problem that describes the large $n$ behavior. We show that for rational values of $\theta$ there is an equivalent vector equilibrium problem.

Keywords: biorthogonal ensembles; vector equilibrium problem; random matrix theory; logarithmic potential theory.

MSC: 31A05; 60B20

Received: April 12, 2016; in final form July 3, 2016; Published online July 5, 2016

Language: English

DOI: 10.3842/SIGMA.2016.065

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ArXiv: 1604.03070