学术报告报告主题: Conditional thinning and multiplicative statistics of Laguerre-type orthogonal polynomial ensembles
报 告 人: 张仑 教授（复旦大学）
报告时间：2026年7月4日（星期六）下午 14：00-15：00
报告地点：37号楼3A02
邀 请 人: 凌黎明 教授
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数学学院
2026年6月25日
报告摘要：
In this talk, we consider the local statistics of orthogonal polynomial ensembles near a hard edge, subject to a multiplicative deformation of the measure. Probabilistically, this deformation corresponds to a position-dependent conditional thinning of the particles. We prove that, under critical hard edge scaling and for a large class of potentials and deformation symbols, the correlation kernel of the conditional ensemble converges to a universal limit, which we identify as the conditional thinned Bessel point process. We derive an explicit expression for this limiting kernel in terms of the solution to a nonlocal integrable system depending on a parameter. For a special choice of the parameter, this system was recently identified in the study of multiplicative statistics of the Bessel point process. Our results establish that this system governs the full correlation structure of the conditional Bessel point process, extending the classical connection between the standard Bessel kernel and the Painlevé V equation. This talk is based on a joint work with Leslie Molag and Guilherme L. F. Silva.
报告人介绍：
张仑，复旦大学数学科学学院教授，博士毕业于香港城市大学，曾在比利时荷语鲁汶大学从事博士后研究。主要研究领域为：数学物理、随机矩阵理论、Fredholm行列式等。相关研究成果发表在J. London Math. Soc.、Adv. in Math.、SIAM J. Math. Anal.等国际期刊。