题目：Noise Stability: Old and New
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.