Monge solutions and uniqueness in multi-marginal optimal transport with hierarchical jumps
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917246675189760 |
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| author | Xu, Zijian |
| author_facet | Xu, Zijian |
| contents | We introduce Hierarchical Jump multi-marginal transport (HJMOT), a generalization of multi-marginal optimal transport where mass can "jump" over intermediate spaces via augmented isolated points. Established on Polish spaces, the framework guarantees the existence of Kantorovich solutions and, under sequential differentiability and a twist condition, the existence and uniqueness of Monge solutions. This core theory extends robustly to diverse settings, including smooth Riemannian manifolds, demonstrating its versatility as a unified framework for optimal transport across complex geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monge solutions and uniqueness in multi-marginal optimal transport with hierarchical jumps Xu, Zijian Probability Differential Geometry Optimization and Control We introduce Hierarchical Jump multi-marginal transport (HJMOT), a generalization of multi-marginal optimal transport where mass can "jump" over intermediate spaces via augmented isolated points. Established on Polish spaces, the framework guarantees the existence of Kantorovich solutions and, under sequential differentiability and a twist condition, the existence and uniqueness of Monge solutions. This core theory extends robustly to diverse settings, including smooth Riemannian manifolds, demonstrating its versatility as a unified framework for optimal transport across complex geometries. |
| title | Monge solutions and uniqueness in multi-marginal optimal transport with hierarchical jumps |
| topic | Probability Differential Geometry Optimization and Control |
| url | https://arxiv.org/abs/2512.14072 |