Workshop: Asymptotics of biorthogonal polynomials related to Muttalib-Borodin ensemble in the hard to soft transitive re

Speaker
Dong Wang, Chinese Academy of Sciences

Abstract
Muttalib-Borodin ensemble is a typical biorthogonal ensemble, and its correlation kernel is expressed by biorthogonal polynomials. It has a hard edge limit where the limits of the associated biorthogonal polynomials are expressed by Wright’s generalized Bessel functions, or by Meijer G functions if the parameter $\theta$ is an integer. This hard edge limit does not occur in orthogonal polynomial ensembles. In this talk we consider the transition from the hard edge limit to the soft edge limit of the Muttalib-Borodin ensemble with an integer $\theta$ parameter, and find an interpolation from the Meijer G limit to the Airy limit of the biorthogonal polynomials. This is joint work with Shui-Xia Xu.