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arXiv · 1011.4166

A note on Gaussian correlation inequalities for nonsymmetric sets

Adrian P. C. Lim·Dejun Luo
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Abstract

We consider the Gaussian correlation inequality for nonsymmetric convex sets. More precisely, if $A\subset\mathbb{R}^d$ is convex and the origin $0\in A$, then for any ball $B$ centered at the origin, it holds $γ_d(A\cap B)\geq γ_d(A)γ_d(B)$, where $γ_d$ is the standard Gaussian measure on $\mathbb{R}^d$. This generalizes Proposition 1 in [Arch. Rational Mech. Anal. 161 (2002), 257--269].

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Adrian P. C. Lim, Dejun Luo. 2010-11-18. A note on Gaussian correlation inequalities for nonsymmetric sets. https://doi.org/10.1016/j.spl.2011.10.001

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