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Motivated by Talagrand's conjecture on regularization properties of thenatural semigroup on the Boolean hypercube, and in particular its continuousanalogue involving regularization properties of the Ornstein-Uhlenbecksemigroup acting on in-tegrable functions, we explore deviation inequalitiesfor log-semiconvex functions under Gaussian measure.

Deviation inequalities for convex functions motivated by the Talagrand conjecture