On Talagrand's Convolution Conjecture in Gaussian Space

Thursday, April 16, 2015 - 10:30am - 11:20am
Keller 3-180
Ronen Eldan (University of Washington)
We prove that any non-negative function f on Gaussian space that is not too log-concave (namely, a function satisfying Hess(log(f)) > - C Id) has tails strictly better than those given by Markov's inequality:

P(f > c)
where E[f] denotes the (Gaussian) expectation of f. An immediate
consequence is a positive answer to the Gaussian variant of Talagrand's (1989) question about regularization of L^1 functions under the convolution semigroup.
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