非线性可积系统与孤立子理论最新进展研讨会

时间：2024年4月26日 16:00-17:00

地点：西安交通大学兴庆校区数学楼423会议室

报告题目： On the gap probability of the tacnode process

摘要： The tacnode process is a universal determinantal point process arising from non-intersecting particle systems and tiling problems. It is the aim of this talk to explore the integrable structure and asymptotics for the gap probability of the thinned/unthinned tacnode process over $(-s, s)$. We establish an integral representation of the gap probability in terms of the Hamiltonian associated with a system of differential equations. With the aids of some remarkable differential identities for the Hamiltonian, we also compute large gap asymptotics, up to and including the constant term in the thinned case. As direct applications, we obtain expectation, variance and a central limit theorem for the associated counting function.

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。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。主持包括国家自然科学基金优秀青年科学基金在内的多项国家及省部级科研项目。