The existence of geodesics in Wasserstein spaces over path groups and loop groups |
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Authors: | Jinghai Shao |
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Institution: | Center for Applied Mathematics, Tianjin University, Tianjin 300072, China |
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Abstract: | In this work we prove the existence and uniqueness of the optimal transport map for -Wasserstein distance with , and particularly present an explicit expression of the optimal transport map for the case . 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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Keywords: | Monge–Kantorovich problem Path groups Loop groups Heat kernel measure Pinned Wiener measure |
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