Local universality in the Muttalib-Borodin ensembles
报告专家：张仑教授（复旦大学）
报告时间：7月11日（周一）上午9:00-10:00
报告地点：腾讯会议：981 734 082
报告摘要：In this talk, we consider the Muttalib-Borodin ensemble of Laguerre type, a determinantal point process on $[0,\infty)$ which depends on the varying weights $x^{\alpha}e^{-nV(x)}$, $\alpha>-1$, and a parameter $\theta$. For $\theta$ being a positive integer, we derive asymptotics of the associated biorthogonal polynomials near the origin for a large class of potential functions $V$ as $n\to \infty$. This further allows us to establish the hard edge scaling limit of the correlation kernel, which is previously only known in special cases and conjectured to be universal. Our proof is based on a Deift/Zhou nonlinear steepest descent analysis of two $1 \times 2$ vector-valued Riemann-Hilbert problems. Based on a joint work with Dong Wang.
专家简介： 张仑，复旦大学数学科学学院教授，博士生导师。研究方向为随机矩阵理论，Riemann-Hilbert方法与渐进分析，特殊函数与正交多项式等。迄今已在Comm. Pure Appl. Math.，Comm. Math. Phys.，Numer. Math.，SIAM J. Math. Anal.等国际重要学术期刊发表学术论文30余篇。主持包括优秀青年基金在内的多项国家自然科学基金，上海市东方学者、东方学者跟踪计划获得者。
