Calculus of Variations and Geometric Measure Theory

A. Figalli - F. Maggi - A. Pratelli

A Geometric Approach to Correlation Inequalities in the Plane

created by maggi on 28 Jun 2011
modified by pratelli on 16 Feb 2015


Published Paper

Inserted: 28 jun 2011
Last Updated: 16 feb 2015

Journal: Ann. Inst. Henri Poincaré Probab. Stat.
Year: 2012


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, PittÂ’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.