數學學科2021系列學術報告二十一

　　報告人：徐帥俠

　　題目：Gap probability near the cusp singularity in random matrix ensembles

　　時間：2021年9月24日 (星期五),  13:50-14:50

　　騰訊會議 ID：802 744 029

　　摘要：We study the gap probability of finding no eigenvalues near the cusp singularity in random matrix ensembles. It was known that the cusp singularity leads to a new universal determinantal process characterized by the Pearcey kernel. By studying the Pearcey-kernel determinant, we establish an integral representation of the gap probability in terms of the Hamiltonian of a system of nonlinear differential equations. Together with some remarkable differential identities for the Hamiltonian, this allows us to obtain the asymptotics of the gap probability as the size of the gap tends to infinity. This talk is based on joint work with Dan Dai and Lun Zhang.

　　個人簡介：徐帥俠，中山大學教授，主要研究方向是漸近分析、隨機矩陣理論和Painleve方程。主要研究工作發表在Communications in Mathematical Physics、SIAM Journal on Mathematical Analysis 和 Journal of Differential Equations 等期刊。