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Optimal transportation for the determinant

Guillaume Carlier·Bruno Nazaret
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Abstract

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.

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Guillaume Carlier, Bruno Nazaret. 2006-12-06. Optimal transportation for the determinant. https://doi.org/10.1051/cocv%3A2008006

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