Abstract
We consider the Gaussian correlation inequality for nonsymmetric convex sets. More precisely, if A ⊂ R d is convex and the origin 0 ∈ A , then for any ball B centered at the origin, it holds γ d ( A ∩ B ) ≥ γ d ( A ) γ d ( B ) , where γ d is the standard Gaussian measure on R d . This generalizes Proposition 1 in [Cordero-Erausquin, Dario, 2002. Some applications of mass transport to Gaussian-type inequalities. Arch. Ration. Mech. Anal. 161, 257–269].
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