Abstract: In this talk, we will introduce two new bounds related to the Gaussian Ornstein-Uhlenbeck convolution operator, whose proofs heavily rely on the use of Ito calculus. The first bound is a sharp robust estimate for the Gaussian noise stability inequality of Borell (which is, in turn, a generalization of the Gaussian isoperimetric inequality of Borell and Sudakov-Tsirelson). The second bound concerns with the regularization of $L_1$ functions under the convolution operator, and provides an affirmative answer to (the Gaussian version of) a 1989 question of Talagrand. By reviewing some central ideas of the proofs of these bounds, I hope to be able to illustrate the potential power of Ito calculus in proving inequalities with a geometric nature. This is (in part) a joint work with James Lee.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006