A reverse entropy power inequality for i.i.d. log-concave random variables
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914126144471040 |
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| author | Fu, Zhen Li, Jiange |
| author_facet | Fu, Zhen Li, Jiange |
| contents | We show that $h_\infty(X+Y)\leq h_\infty(Z+W)$, where $X, Y$ are independent log-concave random variables, and $Z, W$ are exponential random variables having the same respective $\infty$-Rényi entropies. Analogs for integer-valued monotone log-concave random variables are also obtained. Our main tools are decreasing rearrangement, majorization, and the change of measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09206 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A reverse entropy power inequality for i.i.d. log-concave random variables Fu, Zhen Li, Jiange Probability Information Theory Functional Analysis Metric Geometry We show that $h_\infty(X+Y)\leq h_\infty(Z+W)$, where $X, Y$ are independent log-concave random variables, and $Z, W$ are exponential random variables having the same respective $\infty$-Rényi entropies. Analogs for integer-valued monotone log-concave random variables are also obtained. Our main tools are decreasing rearrangement, majorization, and the change of measure. |
| title | A reverse entropy power inequality for i.i.d. log-concave random variables |
| topic | Probability Information Theory Functional Analysis Metric Geometry |
| url | https://arxiv.org/abs/2510.09206 |