Talagrand's Convolution Conjecture

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Published on ● Video Link: https://www.youtube.com/watch?v=6VsYMF05n5Y


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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).



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