题    目：Wiener chaos decomposition of linear statistics of determinantal point processes

主讲人：姚东 副教授

单    位：江苏师范大学

时    间：2025年4月7日 9:00

地    点：数学院211教室

摘    要：Consider a determinantal point process S and functions f of k variables. The linear statistic Lf is defined by the sum of f(x_1,…,x_k) over all possible combinations of pairwise distinct points x_1,…,x_k in S. When k=1 (f is a univariable function), Soshnikov established a combinatorial identity to represent the cumulants of Lf, using which he proved a central limit theorem for linear statistics under general conditions. We generalize this identity to multivariable functions and use this tool to analyze the Wiener chaos decomposition of multivariate statistics of the spherical harmonic ensemble and the infinite Ginibre ensemble.

简    介：姚东，江苏师范大学数学研究院副教授。主要研究兴趣为随机矩阵、随机图和交互粒子系统，论文发表于Ann. Probab.等国际数学期刊。（邀请人: 王玲娣）