Geodesic
Optimal transportation for the determinant
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 678-698

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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.

DOI : 10.1051/cocv:2008006
Classification : 28-99, 49-99
Keywords: optimal transportation, multi-marginals problems, determinant, disintegrations 
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     title = {Optimal transportation for the determinant},
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Carlier, Guillaume; Nazaret, Bruno. Optimal transportation for the determinant. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 678-698. doi: 10.1051/cocv:2008006

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