Optimal transportation for the determinant
CEREMADE, UMR CNRS 7534, Université Paris Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France; firstname.lastname@example.org; email@example.com
Revised: 27 April 2007
Among -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.
Mathematics Subject Classification: 28-99 / 49-99
Key words: Optimal transportation / multi-marginals problems / determinant / disintegrations
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