{"paper":{"title":"Weak limits of entropy regularized Optimal Transport; potentials, plans and divergences","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Alberto Gonzalez-Sanz, Jean-Michel Loubes, Jonathan Niles-Weed","submitted_at":"2022-07-15T12:09:04Z","abstract_excerpt":"This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\\R^d$. We first provide the central limit theorem of the Sinkhorn potentials -- the solutions of the dual problem -- as a Gaussian process in $\\Cs$. Then we obtain the weak limits of the couplings -- the solutions of the primal problem -- evaluated on integrable functions, proving a conjecture of \\cite{ChaosDecom}. In both cases, their limit is a real Gaussian random variable. Finally we consider the weak limit of the entropic Sin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.07427","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.07427/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}