A Vector Equilibrium Problem for Muttalib-Borodin Biorthogonal Ensembles

[摘要] 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.

[关键词] biorthogonal ensembles;vector equilibrium problem;random matrix theory;logarithmic potential theory