Georgia Institute of Technology College of Sciences

A fundamental result in Asymptotic Geometric Analysis is Dvoretzky’s theorem, which asserts that almost euclidean structure is locally present in any high-dimensional normed space. V. MIlman promoted the random version of the “Dvoretzky Theorem” by introducing the “concentration of measure Phenomenon.” Quantifying this phenomenon is important in theory as well as in applications. In this talk  I will explain how techniques from High-dimensional Probability can be exploited to obtain optimal bounds on the randomized Dvoretzky theorem. Based on joint work(s) with Petros Valettas.