报告题目：Multiplicative constant in asymptotic of higher-order Tracy-Widom distribution

报告人：姚鹿鸣 助理教授 深圳大学

报告时间：2026年10月16日 上午10:00-11:00

报告地点：逸夫楼1537

报告摘要：In this talk, we are concerned with higher-order analogues of the Tracy-Widom distribution, which describe the eigenvalue distributions in unitary random matrix models near critical edge points. The associated kernels are constructed by functions related to the even members of the Painlev\'{e} I hierarchy $\mathrm{P_{I}^{2k}}, k\in\mathbb{N}^{+}$, and are regarded as higher-order analogues of the Airy kernel. By performing a uniform asymptotic analysis on the associated Riemann-Hilbert problem, we derive the multiplicative constant in the large gap asymptotics of the distribution, resolving an open problem in the work of Claeys, Its and Krasovsky  for special choice of parameters. An important new feature of the expression is the involvement of an integral of the Hamiltonian associated with a special, real, pole-free solution for $\mathrm{P_{I}^{2k}}$. In addition, we show that the total integral of the Hamiltonian vanishes for all $k$, and establish a transition from the higher-order Tracy-Widom distribution to the classical one in the asymptotic regime. Our approach also works for general parameters and can be adapted to calculate similar critical constants in other problems arising from mathematical physics. 

This talk is based on a joint work with Dan Dai, Wen-Gao Long, Shuai-Xia Xu and Lun Zhang.

报告人简介：姚鹿鸣，现任深圳大学助理教授。2021年于香港城市大学获博士学位，2021年至2024年在复旦大学从事博士后研究，2024年入职深圳大学高等研究院。主要研究方向包括随机矩阵理论、特殊函数的渐近分析等。