Transportation onto log-Lipschitz perturbations

[2305.03786] Transportation onto log-Lipschitz perturbations Skip to main content Search Submit Donate Log in Mathematics > Probability arXiv:2305.03786 (math) [Submitted on 5 May 2023 ( v1 ), last revised 24 Aug 2026 (this version, v3)] Title: Transportation onto log-Lipschitz perturbations Authors: Max Fathi , Dan Mikulincer , Yair Shenfeld View PDF HTML (experimental) Abstract: We establish sufficient conditions for the existence of globally Lipschitz transport maps between probability measures and their log-Lipschitz perturbations, with dimension-free bounds. Our results include Gaussian measures on Euclidean spaces and uniform measures on spheres as source measures. More generally, we prove results for source measures on manifolds satisfying strong curvature assumptions. These seem to be the first examples of dimension-free Lipschitz transport maps in non-Euclidean settings, which are moreover sharp on the sphere. We also present some applications to functional inequalities, including a new dimension-free Gaussian isoperimetric inequality for log-Lipschitz perturbations of the standard Gaussian measure. Our proofs are based on the Langevin flow construction of transport maps of Kim and Milman. Comments: 20 pages. Minor corrections Subjects: Probability (math.PR) ; Analysis of PDEs (math.AP); Functional Analysis (math.FA) MSC classes: 39B62 (Primary) 49Q22, 49R05, 35P15 (Secondary) Cite as: arXiv:2305.03786 [math.PR] (or arXiv:2305.03786v3 [math.PR] for this version) https://doi.org/10.48550/arXiv.2305.03786 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yair Shenfeld [ view email ] [v1] Fri, 5 May 2023 18:37:24 UTC (23 KB) [v2] Mon, 11 Dec 2023 15:27:18 UTC (24 KB) [v3] Mon, 24 Aug 2026 20:17:40 UTC (24 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2023-05 Change to browse by: math math.AP math.FA References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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