Talagrand's Convolution Conjecture
996 views · Published 21 June 2016 · 57:49 · Indexed 14 November 2026
Channel: Microsoft Research · 2016 · Science & Technology
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 L 1 functions under convolution. (Joint work with James Lee).
