Author:

Keywords:

biorthogonal ensembles, vector equilibrium problem, random matrix theory, logarithmic potential theory, Science & Technology, Physical Sciences, Mathematics, Physics, Mathematical, Physics, random matirx theory, ORTHOGONAL POLYNOMIAL ENSEMBLES, POTENTIALS, MATRICES, 0101 Pure Mathematics, 0102 Applied Mathematics, 0105 Mathematical Physics, 4901 Applied mathematics, 4904 Pure mathematics

Abstract:

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