Schramm-Steif Variance Inequalities for Poisson Processes and Noise Sensitivity

Explore a 34-minute lecture on Schramm-Steif variance inequalities for Poisson processes and noise sensitivity. Delve into the analysis of a square-integrable function f(η) of a Poisson process η on a general Borel space, determined by a stopping set Z. Examine the derivation of analogues to Schramm-Steif variance inequalities using the chaos expansion of f(η), originally proven for Boolean functions of independent Rademacher variables. Discover how these inequalities can be applied to study quantitative noise sensitivity and exceptional times for binary functions of η. Investigate the application of these concepts to k-percolation of the Poisson Boolean model with bounded grains, based on joint work with G. Peccati (Luxembourg) and D. Yogeshwaran (Bangalore).