On the Log-Sobolev Constant of Log-Concave Vectors
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914332087943168 |
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| author | Bizeul, Pierre |
| author_facet | Bizeul, Pierre |
| contents | It is well known that if a random vector satisfies a log-Sobolev inequality, all of its marginals have subgaussian tails. In the spirit of the KLS conjecture, we investigate whether this implication can be reversed under a log-concavity assumption. In the general setting, we improve on a result of Bobkov, establishing the best dimension dependent bound on the log-Sobolev constant of subgaussian log-concave measures, and we investigate some special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12997 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Log-Sobolev Constant of Log-Concave Vectors Bizeul, Pierre Functional Analysis Metric Geometry Probability It is well known that if a random vector satisfies a log-Sobolev inequality, all of its marginals have subgaussian tails. In the spirit of the KLS conjecture, we investigate whether this implication can be reversed under a log-concavity assumption. In the general setting, we improve on a result of Bobkov, establishing the best dimension dependent bound on the log-Sobolev constant of subgaussian log-concave measures, and we investigate some special cases. |
| title | On the Log-Sobolev Constant of Log-Concave Vectors |
| topic | Functional Analysis Metric Geometry Probability |
| url | https://arxiv.org/abs/2306.12997 |