Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 065, 15 pages      arXiv:1604.03070
Contribution to the Special Issue on Asymptotics and Universality in Random Matrices, Random Growth Processes, Integrable Systems and Statistical Physics in honor of Percy Deift and Craig Tracy

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

Received April 12, 2016, in final form July 03, 2016; Published online July 05, 2016

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.

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

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