报告人：张仑 教授
报告题目：Confluent hypergeometric kernel determinant on multiple large intervals
报告时间：2026年1月17日（周六）下午14：00
报告地点：云龙校区智华楼205报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
张仑，复旦大学教授，博士生导师，数学科学学院院长助理，国家级科技人才。研究方向为随机矩阵理论，可积系统，Riemann-Hilbert方法与渐近分析，特殊函数与正交多项式等。在随机矩阵特征值分布普适性猜想等领域取得了重要研究成果。相关研究成果发表在Comm. Pure Appl. Math.，Adv. Math., Comm. Math. Phys., J. Funct. Anal.等国际重要学术期刊，主持多项国家自然科学基金及省部级科研项目。
报告摘要：
The confluent hypergeometric point process represents a universality class which arises in a variety of different but related areas. It particularly describes the local statistics of eigenvalues in the bulk of spectrum near a Fisher-Hartwig singular point for a broad class of unitary ensembles. It is the aim of this work to investigate large gap asymptotics of this process over a union of disjoint intervals $\cup_{j=0}^{n}(sa_j,sb_j)$, where $a_0<b_0<\dots<a_m<0<b_m<\dots<a_n<b_n$, for some $0\leq m \leq n$. As $s\to +\infty$, we establish a general asymptotic formula up to and including the oscillatory term of order $1$, which involves a $\theta$- functions-combination integral along a linear flow on an $n$-dimensional torus. If the linear flow has ``good Diophantine properties'' or the ergodic properties, we further improve the error estimate or the leading term for the asymptotics of the integral. These results can be combined for the case $n=1$, which lead to a precise large gap 12asymptotics up to an undetermined constant. Joint work with Taiyang Xu and Zhenyang Zhao.
