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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.18799 |
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| _version_ | 1866916546254733312 |
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| author | Baudoin, Fabrice Gordina, Maria Sarkar, Rohan |
| author_facet | Baudoin, Fabrice Gordina, Maria Sarkar, Rohan |
| contents | We study stability under tensorization and projection-type operations of gradient-type estimates and other functional inequalities for Markov semigroups on metric spaces. Using transportation-type inequalities obtained by F. Baudoin and N. Eldredge in 2021, we prove that constants in the gradient estimates can be chosen to be independent of the dimension. Our results are applicable to hypoelliptic diffusions on sub-Riemannian manifolds and some hypocoercive diffusions. As a byproduct, we obtain dimension-independent reverse Poincaré, reverse logarithmic Sobolev, and gradient bounds for Lie groups with a transverse symmetry and for non-isotropic Heisenberg groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18799 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimension-independent functional inequalities by tensorization and projection arguments Baudoin, Fabrice Gordina, Maria Sarkar, Rohan Probability Analysis of PDEs Functional Analysis Primary 58J35, Secondary 22E30, 28A33, 35A23, 35K08 We study stability under tensorization and projection-type operations of gradient-type estimates and other functional inequalities for Markov semigroups on metric spaces. Using transportation-type inequalities obtained by F. Baudoin and N. Eldredge in 2021, we prove that constants in the gradient estimates can be chosen to be independent of the dimension. Our results are applicable to hypoelliptic diffusions on sub-Riemannian manifolds and some hypocoercive diffusions. As a byproduct, we obtain dimension-independent reverse Poincaré, reverse logarithmic Sobolev, and gradient bounds for Lie groups with a transverse symmetry and for non-isotropic Heisenberg groups. |
| title | Dimension-independent functional inequalities by tensorization and projection arguments |
| topic | Probability Analysis of PDEs Functional Analysis Primary 58J35, Secondary 22E30, 28A33, 35A23, 35K08 |
| url | https://arxiv.org/abs/2403.18799 |