On the Lipschitz properties of transportation along heat flows
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911283734904832 |
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| author | Mikulincer, Dan Shenfeld, Yair |
| author_facet | Mikulincer, Dan Shenfeld, Yair |
| contents | We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim and Milman. For (semi)-log-concave measures and Gaussian mixtures, our bounds have several applications: eigenvalues comparisons, dimensional functional inequalities, and domination of distribution functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_01382 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Lipschitz properties of transportation along heat flows Mikulincer, Dan Shenfeld, Yair Probability Analysis of PDEs Functional Analysis 39B62 (Primary) 49Q22, 49R05, 35P15 (Secondary) We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim and Milman. For (semi)-log-concave measures and Gaussian mixtures, our bounds have several applications: eigenvalues comparisons, dimensional functional inequalities, and domination of distribution functions. |
| title | On the Lipschitz properties of transportation along heat flows |
| topic | Probability Analysis of PDEs Functional Analysis 39B62 (Primary) 49Q22, 49R05, 35P15 (Secondary) |
| url | https://arxiv.org/abs/2201.01382 |