On the Gaussian measure of the intersection of symmetric, convex sets

Details On the Gaussian measure of the intersection of symmetric, convex sets On the Gaussian measure of the intersection of symmetric, convex sets

1996-07-18

arxiv.org/abs/math/9607210v1

Mathematics

Probability

Scientific paper

The Gaussian Correlation Conjecture states that for any two symmetric, convex sets in n-dimensional space and for any centered, Gaussian measure on that space, the measure of the intersection is greater than or equal to the product of the measures. In this paper we obtain several results which substantiate this conjecture. For example, in the standard Gaussian case, we show there is a positive constant, c, such that the conjecture is true if the two sets are in the Euclidean ball of radius $c\sqrt{n}$. Further we show that if for every n the conjecture is true when the sets are in the Euclidean ball of radius $\sqrt{n}$, then it is true in general. Our most concrete result is that the conjecture is true if the two sets are (arbitrary) centered ellipsoids.

Affiliated with

Also associated with

No associations

Rating

On the Gaussian measure of the intersection of symmetric, convex sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Gaussian measure of the intersection of symmetric, convex sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Gaussian measure of the intersection of symmetric, convex sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-673039