An inequality for moments of log-concave functions on Gaussian random vectors

Published 11 Jan 2016 in math.PR | (1601.02492v3)

Abstract: We prove a sharp moment inequality for a log-concave or a log-convex function, on Gaussian random vectors. As an application we take a stability result for the classical logarithmic Sobolev inequality of L. Gross in the case where the function is log-concave.

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