Figalli A, Maggi F, Pratelli A (2014)
Publication Language: English
Publication Status: Published
Publication Type: Journal article
Publication year: 2014
Publisher: Elsevier Masson / Institute Henri Poincaré
Book Volume: 50
Pages Range: 1-14
Journal Issue: 1
DOI: 10.1214/12-AIHP494
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.
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.
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