Tel-Aviv University
School of Mathematical Sciences

Department Colloquium

Monday, December 22, 2014

Schreiber 006, 12:15

Ronen Eldan

University of Washington

Deriving some new inequalities related to the convolution operator on
Gaussian space using stochastic calculus

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