Asymptotics of biorthogonal polynomials related to Muttalib–Borodin ensemble and Hermitian random matrix with external source

报告题目：Asymptotics of biorthogonal polynomials related to Muttalib–Borodin ensemble and Hermitian random matrix with external source

报 告 人：王东，中国科学院大学副教授

报告时间：2025年 11月26日  9:00-11:00

报告地点：数学学院A321

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报告摘要：The Muttalib–Borodin ensemble is a typical biorthogonal ensemble, and its correlation kernel is expressed by biorthogonal polynomials. In this talk we consider the limit of these biorthogonal polynomials, and the limit of the correlation kernel for the Muttalib-Borodin ensemble with an integer $\theta$ parameter. We show that the limits are related to Painleve-type equations in the hard-to-soft transition regime. Our result generalizes the result for Laguerre type random matrix model that is the $\theta = 1$ specialization of Muttalib–Borodin ensemble, in which the limiting correlation kernel is related to the Painleve XXXIV equation in the hard-to-soft transition regime. Moreover, a variation of the biorthogonal polynomials mentioned above is related to a special type of Hermitian random matrix model with external source. We show that the limit of these biorthogonal polynomials yields the Pearcey limit and a higher critical limit of the external source model. This talk is based on joint work with Shuai-Xia Xu.

报告人简介：

王东，中国科学院大学副教授，曾任教于新加坡国立大学，并曾在在密歇根大学做博士后。博士毕业于美国Brandeis大学。在Communications in Mathematical Physics，Annals in Probability等杂志发表过论文。