A geometric approach to correlation inequalities in the plane

Figalli A, Maggi F, Pratelli A (2014)

Publication Language: English

Publication Status: Published

Publication Type: Journal article

Publication year: 2014

Journal

Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques Elsevier Masson / Institute Henri Poincaré

Publisher: Elsevier Masson / Institute Henri Poincaré

Book Volume: 50

Pages Range: 1-14

Journal Issue: 1

DOI: 10.1214/12-AIHP494

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.

Authors with CRIS profile

Aldo Pratelli Lehrstuhl für Analysis

Involved external institutions

Università degli Studi di Firenze / University of Florence IT Italy (IT) University of Texas at Austin US United States (USA) (US)

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.

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