The algebraic degree of the Wasserstein distance
Algebraic Geometry
2024-01-24 v1 Group Theory
Abstract
Given two rational univariate polynomials, the Wasserstein distance of their associated measures is an algebraic number. We determine the algebraic degree of the squared Wasserstein distance, serving as a measure of algebraic complexity of the corresponding optimization problem. The computation relies on the structure of a subpolytope of the Birkhoff polytope, invariant under a transformation induced by complex conjugation.
Keywords
Cite
@article{arxiv.2401.12735,
title = {The algebraic degree of the Wasserstein distance},
author = {Chiara Meroni and Bernhard Reinke and Kexin Wang},
journal= {arXiv preprint arXiv:2401.12735},
year = {2024}
}
Comments
17 pages, 3 figures