Talagrand’s Convolution Conjecture


August 13, 2014


Tools from James Lee’s July 28 talk will be employed to prove the following: Any non-negative function f on Gaussian space that is not too log-concave has tails strictly better than those given by Markov’s inequality: P(f > c) < E[f]/(c (log c)1/6) where E[f] denotes the (Gaussian) expectation of f. An immediate consequence is a positive answer to Talagrand’s (1989) question about regularization of L1 functions under convolution. (Joint work with James Lee).


Ronen Eldan

Ronen Eldan received his Ph.D from Tel Aviv University, under the supervision of Prof. V. Milman and Prof. B. Klartag, specializing in probability, high dimensional convex geometry and computational geometry. Later, he was a Post-Doctoral fellow at the Weizmann Institute of Science and is currently a visiting researcher at MSR. In the fall he will be a postdoc at UW and next year he will be a Clay Research fellow at NYU.