Tropical optimal transport and Wasserstein distances

@article{Lee2019TropicalOT,
  title={Tropical optimal transport and Wasserstein distances},
  author={Wonjun Lee and Wuchen Li and Bo Lin and Anthea Monod},
  journal={arXiv: Optimization and Control},
  year={2019}
}
We study the problem of optimal transport in tropical geometry and define the Wasserstein-$p$ distances for probability measures in the continuous metric measure space setting of the tropical projective torus. We specify the tropical metric---a combinatorial metric that has been used to study of the tropical geometric space of phylogenetic trees---as the ground metric and study the cases of $p = 1, 2$ in detail. The case of $p = 1$ gives an efficient way to compute geodesics on the tropical… 
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