Busemann functions on the Wasserstein space

Guomin Zhu; Wen-Long Li; Xiaojun Cui

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arXiv · 1905.05544

Busemann functions on the Wasserstein space

Guomin Zhu·Wen-Long Li·Xiaojun Cui

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Abstract

We study rays and co-rays in the Wasserstein space $P_p(\mathcal{X})$ ($p > 1$) whose ambient space $\mathcal{X}$ is a complete, separable, non-compact, locally compact length space. We show that rays in the Wasserstein space can be represented as probability measures concentrated on the set of rays in the ambient space. We show the existence of co-rays for any prescribed initial probability measure. We introduce Busemann functions on the Wasserstein space and show that co-rays are negative gradient lines in some sense.

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BibTeX RIS

Guomin Zhu, Wen-Long Li, Xiaojun Cui. 2019-10-14. Busemann functions on the Wasserstein space. https://arxiv.org/abs/1905.05544

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