A geometric approach to correlation inequalities in the plane

Journal article


Publication Details

Author(s): Figalli A, Maggi F, Pratelli A
Journal: Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques
Publisher: Elsevier Masson / Institute Henri Poincaré
Publication year: 2014
Volume: 50
Journal issue: 1
Pages range: 1-14
ISSN: 0246-0203
Language: English


Abstract


By elementary geometric arguments, correlation inequalities for radially symmetric probability measures are proved in the plane. Precisely, it is shown that the correlation ratio for pairs of width-decreasing sets is minimized within the class of infinite strips. Since open convex sets which are symmetric with respect to the origin turn out to be width-decreasing sets, Pitt's Gaussian correlation inequality (the two-dimensional case of the long-standing Gaussian correlation conjecture) is derived as a corollary, and it is in fact extended to a wide class of radially symmetric measures.



FAU Authors / FAU Editors

Pratelli, Aldo Prof.
Lehrstuhl für Mathematik


External institutions with authors

Università degli Studi di Firenze / University of Florence
University of Texas at Austin


How to cite

APA:
Figalli, A., Maggi, F., & Pratelli, A. (2014). A geometric approach to correlation inequalities in the plane. Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques, 50(1), 1-14. https://dx.doi.org/10.1214/12-AIHP494

MLA:
Figalli, Alessio, Francesco Maggi, and Aldo Pratelli. "A geometric approach to correlation inequalities in the plane." Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques 50.1 (2014): 1-14.

BibTeX: 

Last updated on 2019-21-07 at 07:59