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October 1999 A Particular Case of Correlation Inequality for the Gaussian Measure
Gilles Hargé
Ann. Probab. 27(4): 1939-1951 (October 1999). DOI: 10.1214/aop/1022874822


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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Gilles Hargé. "A Particular Case of Correlation Inequality for the Gaussian Measure." Ann. Probab. 27 (4) 1939 - 1951, October 1999.


Published: October 1999
First available in Project Euclid: 31 May 2002

zbMATH: 0962.28013
MathSciNet: MR1742895
Digital Object Identifier: 10.1214/aop/1022874822

Primary: 28C20 , 60E15

Keywords: Correlation , Gaussian measure , Key words and phrases , Log-concavity , semigroups

Rights: Copyright © 1999 Institute of Mathematical Statistics

Vol.27 • No. 4 • October 1999
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