Monotonicity properties of optimal transportation and the FKG and related inequalities

Authors
Caffarelli, LA
Citation
La. Caffarelli, Monotonicity properties of optimal transportation and the FKG and related inequalities, COMM MATH P, 214(3), 2000, pp. 547-563
Citations number
12
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616 → ACNP
Volume
214
Issue
3
Year of publication
2000
Pages
547 - 563
Database
ISI
SICI code
0010-3616(200011)214:3<547:MPOOTA>2.0.ZU;2-M
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 mo notonicity 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 generalization of the Brascamp-Lieb momentum inequalities.