Grand-Canonical Optimal Transport
arXiv:2201.06859 · doi:10.1007/s00205-024-02080-x
Abstract
We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible 's, while fixing a certain linear combination of the corresponding marginals.
Final version, to appear in Arch. Rat. Mech. Anal