Logarithmic Sobolev inequalities for generalised Cauchy measures
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908934935150592 |
|---|---|
| author | Huguet, Baptiste Nicolas |
| author_facet | Huguet, Baptiste Nicolas |
| contents | We prove a curvature-dimension criterion and obtain logarithmic Sobolev inequalities for generalised Cauchy measures with optimal weights and explicit constants. In the one-dimensional case, this constant is even optimal. From these inequalities, we derive concentration results, which allow concluding the case of the pathological dimension two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17239 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logarithmic Sobolev inequalities for generalised Cauchy measures Huguet, Baptiste Nicolas Functional Analysis Probability We prove a curvature-dimension criterion and obtain logarithmic Sobolev inequalities for generalised Cauchy measures with optimal weights and explicit constants. In the one-dimensional case, this constant is even optimal. From these inequalities, we derive concentration results, which allow concluding the case of the pathological dimension two. |
| title | Logarithmic Sobolev inequalities for generalised Cauchy measures |
| topic | Functional Analysis Probability |
| url | https://arxiv.org/abs/2411.17239 |