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arXiv · 1912.04945

1-Wasserstein Distance on the Standard Simplex

Andrew Frohmader·Hans Volkmer
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Abstract

Wasserstein distances provide a metric on a space of probability measures. We consider the space $Ω$ of all probability measures on the finite set $χ= \{1, \dots ,n\}$ where $n$ is a positive integer. 1-Wasserstein distance, $W_1(μ,ν)$ is a function from $Ω\times Ω$ to $[0,\infty)$. This paper derives closed form expressions for the First and Second moment of $W_1$ on $Ω\times Ω$ assuming a uniform distribution on $Ω\times Ω$.

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Andrew Frohmader, Hans Volkmer. 2019-12-10. 1-Wasserstein Distance on the Standard Simplex. https://doi.org/10.2140/astat.2021.12.43

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