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A geometric approach to correlation inequalities in the plane. (English. French summary) Zbl 1288.60024

Summary: 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.

MSC:

60E15 Inequalities; stochastic orderings
52A40 Inequalities and extremum problems involving convexity in convex geometry
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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References:

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