Probability Seminars——The Lyons-Peres conjecture
主 题: Probability Seminars——The Lyons-Peres conjecture
报告人: 邱彦奇 副研究员 (中科院数学与系统科学院)
时 间: 2017-12-18 15:00-16:00
地 点: Room 1418, Sciences Building No. 1
Abstract: I will explain the Lyons-Peres conjecture in the theory of determinantal point processes (DPP). This conjecture asks certain completeness of all DPP’s with orthogonal projection correlation kernels. For instance, in a particular case, it asks whether almost surely the random set of zeros of the Gaussian random analytic function on the unit disk is the set of uniqueness for the Bergman space. Recently, in a joint work with Alexander Bufetov and Alexander Shamov, we solve completely the Lyons-Peres conjecture. Our method is based on proving the existence and a new local property of conditional correlation kernels for conditional DPP’s.