Among -valued triples of random vectors having fixed marginal probability laws, what is the best way to jointly draw in such a way that the simplex generated by 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.
Keywords: optimal transportation, multi-marginals problems, determinant, disintegrations
@article{COCV_2008__14_4_678_0, author = {Carlier, Guillaume and Nazaret, Bruno}, title = {Optimal transportation for the determinant}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {678--698}, publisher = {EDP-Sciences}, volume = {14}, number = {4}, year = {2008}, doi = {10.1051/cocv:2008006}, mrnumber = {2451790}, zbl = {1160.49015}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2008006/} }
TY - JOUR AU - Carlier, Guillaume AU - Nazaret, Bruno TI - Optimal transportation for the determinant JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 678 EP - 698 VL - 14 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008006/ DO - 10.1051/cocv:2008006 LA - en ID - COCV_2008__14_4_678_0 ER -
%0 Journal Article %A Carlier, Guillaume %A Nazaret, Bruno %T Optimal transportation for the determinant %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 678-698 %V 14 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008006/ %R 10.1051/cocv:2008006 %G en %F COCV_2008__14_4_678_0
Carlier, Guillaume; Nazaret, Bruno. Optimal transportation for the determinant. ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 4, pp. 678-698. doi : 10.1051/cocv:2008006. http://archive.numdam.org/articles/10.1051/cocv:2008006/
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