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Talagrand's Convolution Conjecture

Speaker  Ronen Eldan

Affiliation  MSR

Host  Yuval Peres

Duration  00:57:28

Date recorded  29 July 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).

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