Javascript must be enabled

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!).

Please select playlist name from following

Report Video

Please select the category that most closely reflects your concern about the video, so that we can review it and determine whether it violates our Community Guidelines or isn’t appropriate for all viewers. Abusing this feature is also a violation of the Community Guidelines, so don’t do it.


Comments Disabled For This Video