Isoperimetric Games

Tuesday, May 3, 2016 - 4:00pm

Event Calendar Category

LIDS Seminar Series

Speaker Name

Ramon van Handel

Affiliation

Princeton University

Building and Room Number

32-155

Abstract

That the ball has the smallest surface area among all bodies of equal volume was already known (it is said) to Dido, queen of Carthage. This isoperimetric property follows from the fact that Lebesgue measure is log-concave. The analogous statement for Gaussian distributions - that half-spaces have the smallest Gaussian surface area among all sets of the same probability -plays an important role in high-dimensional probability. However, Gaussian isoperimetry does not follow from log-concavity of the Gaussian distribution, but from a much more delicate convexity property of Gaussian measures known as Ehrhard's inequality. My aim in this talk is to exhibit an unexpected link between Ehrhard's inequality and game theory: the convexity of Gaussian measures arises as the result of a remarkable game between two players who compete for control of a Brownian motion. This approach makes it possible to derive new geometric inequalities for Gaussian measures.

Biography

Ramon van Handel is an Associate Professor in ORFE and in the Program for Applied and Computational Mathematics at Princeton University.  His research interests lie broadly in probability theory and its interactions with other areas of mathematics and its applications. He received the PhD degree from the California Institute of Technology in 2007, and joined the Princeton faculty in 2009.  Selected honors include the NSF CAREER award and a PECASE award, the Erlang prize, the Princeton University Graduate Mentoring Award, and several Excellence in Teaching awards.

Reception information

Reception to follow.