Critical Hermitian matrix model with external source and Boussinesq hierarchy
数学专题报告
报告题目(Title)：Critical Hermitian matrix model with external source and Boussinesq hierarchy
报告人(Speaker)：徐帅侠 教授（中山大学）
地点(Place)：腾讯会议：489 405 062 密码：629792
时间(Time)：2025年12月25日（周四）9:00-10:00
邀请人(Inviter)：王灯山、臧立名
报告摘要
We consider the random Hermitian matrix model with external source and quartic potential $V(x) = \frac{x^4}{4}-t\frac{x^2}{2}$, where the external source $A$ has two eigenvalues $\pm a$ of equal multiplicities. We investigate the limiting local statistics of the eigenvalues of $M$ around $0$ in certain critical regimes as the size of matrix $n \to \infty$. When the parameters $t$ and $a$ lie on a critical curve along which the limiting mean eigenvalue density vanishes as $|x|^{1/3}$, the double scaling limit of the correlation kernel is constructed out of functions associated with the Boussinesq equation. This new limiting kernel reduces to the classical Pearcey kernel when $\alpha=0$. Furthermore, in the multi-critical case where the limiting mean eigenvalue density vanishes as $|x|^{5/3}$, the limiting kernel is built out of the second member of the Boussinesq hierarchy. This talk is based on joint work with Dong Wang.
主讲人简介
徐帅侠，中山大学教授，博士生导师，研究方向为随机矩阵理论、潘勒韦方程、可积系统和渐近分析。主持国家自然科学基金面上项目和广东省杰出青年基金项目等课题。相关结果发表于Comm. Math. Phys.、Adv. Math.、和SIAM JMA等期刊。
