A Vector Equilibrium Problem for Muttalib-Borodin Biorthogonal Ensembles

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.

References in corpus (4)

• Muttalib--Borodin ensembles in random matrix theory --- realisations and correlation functions
• Asymptotic zero distribution of Jacobi-Piñeiro and multiple Laguerre polynomials
• An equilibrium problem for the limiting eigenvalue distribution of banded Toeplitz matrices
• Large deviations principle for biorthogonal ensembles and variational formulation for the Dykema-Haagerup distribution

Cited by in corpus (4)

• The local universality of Muttalib-Borodin biorthogonal ensembles with parameter $\theta =\frac{1}{2}$
• On Wright's generalized Bessel kernel
• Matrix-valued orthogonal polynomials related to hexagon tilings
• The local universality of Muttalib-Borodin ensembles when the parameter $\theta$ is the reciprocal of an integer