题目:
Integrability of biorthogonal polynomials related to Muttalib–Borodin ensemble and Hermitian random matrix with external source
报告人: 王东副教授 (中国科学院大学)
报告时间: 2025年11月11日（周二）上午 9:00--10:00
报告地点: 数学系理科楼A304
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 Shui-Xia Xu.
邀请人：张友金
