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# Elizabeth Meckes : Projections of probability distributions: a measure-theoretic Dvoretzky theorem

Dvoretzky's theorem tells us that if we put an arbitrary norm on n-dimensional Euclidean space, no matter what that normed space is like, if we pass to subspaces of dimension about log(n), the space looks pretty much Euclidean. A related measure-theoretic phenomenon has long been observed: the (one-dimensional) marginals of many natural high-dimensional probability distributions look about Gaussian. A question which had received little attention until recently is whether this phenomenon persists for k-dimensional marginals for k growing with n, and if so, for how large a k? In this talk I will discuss recent work showing that the phenomenon does indeed persist if k less than 2log(n)/log(log(n)), and that this bound is sharp (even the 2!).

**Category**: Probability**Duration**: 01:34:53**Date**: April 4, 2013 at 4:25 PM-
**Tags:**seminar, Probability Seminar

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