OPTIMAL TRANSPORTATION FOR THE DETERMINANT

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 trans- portation problems with several marginals when the objective function is the determinant or its absolute value. Mathematics Subject Classification. 28-99, 49-99.