OPTIMAL TRANSPORTATION FOR THE DETERMINANT

By Guillaume Carlier, Bruno Nazaret. 2006

57 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5d5ca2e76bdecc5c3c393b1ac349b0bfec431a03

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In Applied Mathematics

1. Filippo Santambrogio
2. Brendan Pass
3. Young-Heon Kim
4. Thierry Klein
5. Jérémie Bigot
6. Pratik Chaudhari
7. Stefano Soatto

In Geometry and Topology

1. Filippo Santambrogio
2. Brendan Pass
3. Pratik Chaudhari
4. Stefano Soatto

Citations in the corpus

• Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, background): “We observe that we already faced several examples of “symmetric” cost functions, meaningful when the marginals are identical (which is not the case for the costs in [178] and [110]).”
• Multi-marginal optimal transport: theory and applications (2014, background): “This class includes the Gangbo−Swiech cost ∑mi=1 |xi−xj |2 [36], the determinant cost of Carlier and Nazaret [14], −det(x1x2 .”