Optimal transportation for the determinant

Details Optimal transportation for the determinant Optimal transportation for the determinant

2006-12-06

arxiv.org/abs/math/0612142v1

ESAIM - Control Optimisation and Calculus of Variations 14, 4 (2008) p678-698

Mathematics

Optimization and Control

Scientific paper

10.1051/cocv:2008006

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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