تقرير
Sharp estimates for the Cram\'{e}r transform of log-concave measures and geometric applications
| العنوان: | Sharp estimates for the Cram\'{e}r transform of log-concave measures and geometric applications |
|---|---|
| المؤلفون: | Brazitikos, Silouanos, Chasapis, Giorgos |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Functional Analysis, Mathematics - Metric Geometry, 60D05, 60E15, 52A22, 52A23 |
| الوصف: | 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 Cram\'{e}r 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.07253 |
| رقم الأكسشن: | edsarx.2405.07253 |
| قاعدة البيانات: | arXiv |
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