题目：Noise Stability: Old and New
报告人：于磊（南开大学统计与数据科学学院）
时间：2022年7月13日（星期三），14:00-15:30
地点：哈工大明德楼B区201报告厅
腾讯会议：会议号：963-510-573，链接：https://meeting.tencent.com/dm/b4bebh0wnduo
摘要：Give a joint probability measure, the noise stability problem is to estimate the joint measure of a pair of sets (A, B) given the marginal measures of A and B. In this talk, we will survey classic and recent advances on the noise stability problem, including several important conjectures and open problems and their (partial) solutions, e.g., Mossel's mean-1/4 stability problem (2017), Ordentlich-Polyanskiy-Shayevitz's conjecture (2020), etc. We will also discuss the connection between the noise stability problem and a class of well-known functional inequalities-Brascamp-Lieb (or hypercontractivity) inequalities. This class of inequalities was widely used in probability, combinatorics, computer science, and functional analysis. If time is enough, we introduce proof ideas of these results, and also extend the noise stability to the q-stability.
