# 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…

## 2 Citations

Tropical Geometric Variation of Phylogenetic Tree Shapes

- Mathematics
- 2020

We study the behavior of phylogenetic tree shapes in the tropical geometric interpretation of tree space. Tree shapes are formally referred to as tree topologies; a tree topology can also be thought…

An Invitation to Tropical Alexandrov Curvature

- Mathematics
- 2021

We study Alexandrov curvature in the tropical projective torus with respect to the tropical metric. Alexandrov curvature is a generalization of classical Riemannian sectional curvature to more…

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