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].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.