A brief introduction to determinantal point processes
数学专题报告
报告题目(Title)：A brief introduction to determinantal point processes
报告人(Speaker)：邱彦奇 教授（武汉大学）
地点(Place)：J8-110，腾讯会议ID：484-9383-9680，密码：963852
时间(Time)：2022年10月11日，18日，25日，15:30-17:10
邀请人(Inviter)：陈昕昕
报告摘要
The theory of determinantal point processes was first introduced by Macchi in her studies of random Fermion Fields in 1970's. This theory has latter been extensively studied in various different mathematical areas such as Random Matrices, Random Young Diagrams, Random Holomorphic Functions, Random Graphs etc. In this course, we present an introduction to determinantal point processes, focusing on multiplicative functionals, Palm theory, conditional measures and Ghosh-Peres number rigidity. Specifically, we will try to cover the following topics.
1. Basic examples and definitions of determinantal point processes
2. Fredholm determinants and multiplicative functionals
3. Limit theorems for determinantal point processes
4. Ghosh-Peres number rigidity of determinantal point processes
5. Palm theory and conditional measures
6. Quasi-symmetries of determinantal point processes
7. Determinantal point processes and reproducing kernel Hilbert spaces of holomorphic functions
8. Lyons-Peres conjecture for determinantal point processes
