Sharp estimates for the Cramér transform of log-concave measures and geometric applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915344318201856 |
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| author | Brazitikos, Silouanos Chasapis, Giorgos |
| author_facet | Brazitikos, Silouanos Chasapis, Giorgos |
| contents | We establish a new comparison between the Legendre transform of the cumulant generating function and the half-space depth of an arbitrary log-concave probability distribution on the real line, that carries on to the multidimensional setting. Combined with sharp estimates for the Cramér transform of rotationally invariant measures, we are led to some new phase-transition type results for the asymptotics of the expected measure of random polytopes. As a byproduct of our analysis, we address a question on the sharp exponential separability constant for log-concave distributions, in the symmetric case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07253 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp estimates for the Cramér transform of log-concave measures and geometric applications Brazitikos, Silouanos Chasapis, Giorgos Probability Functional Analysis Metric Geometry 60D05, 60E15, 52A22, 52A23 We establish a new comparison between the Legendre transform of the cumulant generating function and the half-space depth of an arbitrary log-concave probability distribution on the real line, that carries on to the multidimensional setting. Combined with sharp estimates for the Cramér transform of rotationally invariant measures, we are led to some new phase-transition type results for the asymptotics of the expected measure of random polytopes. As a byproduct of our analysis, we address a question on the sharp exponential separability constant for log-concave distributions, in the symmetric case. |
| title | Sharp estimates for the Cramér transform of log-concave measures and geometric applications |
| topic | Probability Functional Analysis Metric Geometry 60D05, 60E15, 52A22, 52A23 |
| url | https://arxiv.org/abs/2405.07253 |