{"paper":{"title":"Structure of martingale transports in finite dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jan Ob\\l\\'oj, Pietro Siorpaes","submitted_at":"2017-02-27T18:52:04Z","abstract_excerpt":"We study the structure of martingale transports in finite dimensions. We consider the family $\\mathcal{M}(\\mu,\\nu) $ of martingale measures on $\\mathbb{R}^N \\times \\mathbb{R}^N$ with given marginals $\\mu,\\nu$, and construct a family of relatively open convex sets $\\{C_x:x\\in \\mathbb{R}^N \\}$, which forms a partition of $\\mathbb{R}^N$, and such that any martingale transport in $\\mathcal{M}(\\mu,\\nu) $ sends mass from $x$ to within $\\overline{C_x}$, $\\mu(dx)$--a.e. Our results extend the analogous one-dimensional results of M. Beiglb\\\"ock and N. Juillet (2016) and M. Beiglb\\\"ock, M. Nutz, and N. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08433","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}