| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1152241 | Statistics & Probability Letters | 2012 | 7 Pages |
Abstract
We consider the Gaussian correlation inequality for nonsymmetric convex sets. More precisely, if A⊂RdA⊂Rd is convex and the origin 0∈A0∈A, then for any ball BB centered at the origin, it holds γd(A∩B)≥γd(A)γd(B)γd(A∩B)≥γd(A)γd(B), where γdγd is the standard Gaussian measure on RdRd. 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].
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Adrian P.C. Lim, Dejun Luo,