The existence of geodesics in Wasserstein spaces over path groups and loop groups

Jinghai Shao

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arXiv · 1802.10226

The existence of geodesics in Wasserstein spaces over path groups and loop groups

Jinghai Shao

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Abstract

In this work we prove the existence and uniqueness of the optimal transport map for $L^p$-Wasserstein distance with $p>1$, and particularly present an explicit expression of the optimal transport map for the case $p=2$. As an application, we show the existence of geodesics connecting probability measures satisfying suitable condition on path groups and loop groups.

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Jinghai Shao. 2018-02-28. The existence of geodesics in Wasserstein spaces over path groups and loop groups. https://arxiv.org/abs/1802.10226

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