The Annals of Probability

A Particular Case of Correlation Inequality for the Gaussian Measure

Gilles Hargé

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Our purpose is to prove a particular case of a conjecture concerning the Gaussian measure of the intersection of two symmetric convex sets of $\mathbb{R}^n$. This conjecture states that the measure of the intersection is greater or equal to the product of the measures. In this paper, we prove the inequality when one of the two convex sets is a symmetric ellipsoid and the other one is simply symmetric. The general case is still open.

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Ann. Probab., Volume 27, Number 4 (1999), 1939-1951.

First available in Project Euclid: 31 May 2002

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Primary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 60E15: Inequalities; stochastic orderings

Key words and phrases Gaussian measure correlation log-concavity semigroups


Hargé, Gilles. A Particular Case of Correlation Inequality for the Gaussian Measure. Ann. Probab. 27 (1999), no. 4, 1939--1951. doi:10.1214/aop/1022874822.

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