On marginals of high-dimensional probability measures

Thursday, March 15, 2018 - 3:30pm
111 Math Science Building
Grigoris Paouris (Texas A&M)

Several results from classical probability theory imply that a "typical" marginal of a product measure is "close" to a Gaussian distribution. The Berry-Essen theorem quantifies this proximity, while Bernstein's inequality gives sub-Gaussian bounds (under mild moments assumptions).  I will review several recent results which show that a typical marginal of a high dimensional probability measure - not necessarily a product - has similar properties. I will explain how geometric ideas can be used to establish central limit theorems, sub-Gaussian behavior and sharp small ball probabilities.

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