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Monotonicity Properties of Optimal Transportation¶and the FKG and Related Inequalities

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Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract:

Optimal transportation between densities f(X), g(Y) can be interpreted as a joint probability distribution with marginally f(X), and g(Y). We prove monotonicity and concavity properties of optimal transportation (Y(X)) under suitable assumptions on f and g. As an application we obtain the Fortuin, Kasteleyn, Ginibre correlation inequalities as well as some generalizations of the Brascamp–Lieb momentum inequalities.

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas at Austin, Austin, TX 78712-1082, USA.¶E-mail: caffarel@math.utexas.edu, , , , , , US

    Luis A. Caffarelli

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  1. Luis A. Caffarelli
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Received: 18 October 1999 / Accepted: 24 March 2000

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Caffarelli, L. Monotonicity Properties of Optimal Transportation¶and the FKG and Related Inequalities. Commun. Math. Phys. 214, 547–563 (2000). https://doi.org/10.1007/s002200000257

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  • DOI: https://doi.org/10.1007/s002200000257

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