Optimal transportation for the determinant

Carlier, Guillaume; Nazaret, Bruno

Carlier, Guillaume; Nazaret, Bruno (2008), Optimal transportation for the determinant, ESAIM. COCV, 14, 4, p. 678-698. http://dx.doi.org/10.1051/cocv:2008006

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00118459/en/

Date

2008

Journal name

ESAIM. COCV

Volume

Number

Publisher

EDP Sciences

Pages

678-698

Abstract (EN)

Among $\R^3$-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.

Subjects / Keywords

Optimal transportation; multi-marginals problems; determinant; disintegrations