The Ehrhard-Borell inequality and hypoelliptic diffusions

High Dimensional Seminar
Wednesday, October 30, 2019 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 006
Yair Shenfeld – Princeton University – yairs@princeton.edu
Galyna Livshyts

The Ehrhard-Borell inequality stands at the top of the pyramid of Gaussian inequalities. It is a powerful and delicate statement about the convexity of the Gaussian measure. In this talk I will discuss the inequality and its beautiful proof by Borell. The delicate nature of the inequality however makes the characterization of the equality cases difficult and they were left unknown. I will explain how we solved this problem. Joint work with Ramon van Handel.