Probability Seminar

Date: April 24, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Alexandros Eskenazis, Princeton

Title: Gaussian mixtures and geometric inequalities

Abstract: A random variable $X$ is called a (centered) Gaussian mixture if there exist a positive random variable $Y$ and a standard Gaussian random variable $Z$, independent of $Y$, such that $X$ has the same distribution as the product $YZ$. We will explain how Gaussian mixtures appear in various extremization problems originating in probability and convex geometry. Examples include finding sharp constants in Khintchine-type inequalities and identifying extremal sections and projections of the unit ball of $\ell_p^n$ with respect to different geometric parameters, such as volume and mean width. Time permitting, we'll also discuss a correlation inequality on the Euclidean sphere. The talk is based on joint work with P. Nayar and T. Tkocz.