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Optimal transportation for the determinant

Published online by Cambridge University Press:  18 January 2008

Guillaume Carlier and
Bruno Nazaret
Guillaume Carlier
Affiliation:
CEREMADE, UMR CNRS 7534, Université Paris Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France; carlier@ceremade.dauphine.fr; nazaret@ceremade.dauphine.fr
Bruno Nazaret
Affiliation:
CEREMADE, UMR CNRS 7534, Université Paris Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France; carlier@ceremade.dauphine.fr; nazaret@ceremade.dauphine.fr
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Abstract

Among ${\mathbb R}^3$ -valued triples of random vectors (X,Y,Z) having fixed marginal probability laws, what is the best way to jointly draw (X,Y,Z) in such a way that the simplex generated by (X,Y,Z) has maximal average volume? Motivated by this simple question, we study optimal transportation problems with several marginals when the objective function is the determinant or its absolute value.

Keywords

Optimal transportationmulti-marginals problemsdeterminantdisintegrations

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 4 , October 2008, pp. 678 - 698
Copyright
© EDP Sciences, SMAI, 2008

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