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学术报告六十一:Tracy-Widom distributions in critical unitary random

来源:数学与统计学院     作者:     时间:2018/6/29 18:06:35  0次

数学与统计学院学术报告[2018]061

(高水平大学建设系列报告180)

讲座题目: Tracy-Widom distributions in critical unitary random matrix ensembles and the coupled Painleve II system

讲座人:Dan Dai (香港城市大学)

讲座时间: 201871  16:00-17:00

讲座地点:科技楼514

报告内容:

We study Fredholm determinants of the Painleve II and Painleve XXXIV kernels. In certain critical unitary random matrix ensembles, these determinants describe special gap probabilities of eigenvalues. We obtain Tracy-Widom formulas for the Fredholm determinants, which are explicitly given in terms of integrals involving a family of distinguished solutions to the coupled Painleve II system in dimension four. Moreover, the large gap asymptotics for these Fredholm determinants are derived, where the constant terms are given explicitly in terms of the Riemann zeta-function.

报告人简历:

Dr. Dan Dai is an associate professor at Department of Mathematics, City University of Hong Kong. He received his BSc from Fudan University and PhD from City University of Hong Kong. Before joining City University in 2008, he worked as a postdoctoral fellow at Katholieke Universiteit Leuven, Belgium. His major research interests include asymptotic analysis, special functions, orthogonal polynomials, Riemann-Hilbert problems and random matrix theory. So far he has published about 20 research papers in international journals, including Communications in Mathematical Physics, Nonlinearity, SIAM Journal on Mathematical Analysis, Studies in Applied Mathematics, etc.

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