A note on Gaussian correlation inequalities for nonsymmetric sets

Adrian P.C. Lim and Dejun Luo

Statistics & Probability Letters, 2012, vol. 82, issue 1, 196-202

Abstract: We consider the Gaussian correlation inequality for nonsymmetric convex sets. More precisely, if A⊂Rd is convex and the origin 0∈A, then for any ball B centered at the origin, it holds γd(A∩B)≥γd(A)γd(B), where γd is the standard Gaussian measure on Rd. 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].

Keywords: Correlation inequality; Gaussian measure; Convexity; Log-concavity; Optimal transport (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2011.10.001

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