Guenter Last: Schramm-Steif variance inequalities for Poisson processes and noise sensitivity

Описание к видео Guenter Last: Schramm-Steif variance inequalities for Poisson processes and noise sensitivity

Consider a Poisson process η on a general Borel space. Suppose that a square-integrable function f(η) of η is determined by a stopping set Z. Based on the chaos expansion of f(η) we shall de rive analogues of the Schramm-Steif variance inequalities (proved for Boolean functions of independent Rademacher variables). We will show how these inequalities can be used to study quantitative noise sensitivity and exceptional times for binary functions of η. As an application we discuss k-percolation of the Poisson Boolean model with bounded grains. This is joint work with G. Peccati (Luxembourg) and D. Yogeshwaran (Bangalore).

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