{"paper":{"title":"Gluing methods for quantitative stability of optimal transport maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Cyril Letrouit, Quentin M\\'erigot","submitted_at":"2024-11-07T17:48:49Z","abstract_excerpt":"We establish quantitative stability bounds for the quadratic optimal transport map $T_\\mu$ between a fixed probability density $\\rho$ and a probability measure $\\mu$ on $\\mathbb{R}^d$. Under general assumptions on $\\rho$, we prove that the map $\\mu\\mapsto T_\\mu$ is bi-H\\\"older continuous, with dimension-free H\\\"older exponents. The linearized optimal transport metric $W_{2,\\rho}(\\mu,\\nu)=\\|T_\\mu-T_\\nu\\|_{L^2(\\rho)}$ is therefore bi-H\\\"older equivalent to the $2$-Wasserstein distance, which justifies its use in applications.\n  We show this property in the following cases: (i) for any log-concav"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.04908","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/2411.04908/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"}