Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2501.10309 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929680743923712 |
|---|---|
| author | Fradelizi, Matthieu Gavalakis, Lampros Rapaport, Martin |
| author_facet | Fradelizi, Matthieu Gavalakis, Lampros Rapaport, Martin |
| contents | We establish analogues of the Bergström and Bonnesen inequalities, related to determinants and volumes respectively, for the entropy power and for the Fisher information. The obtained inequalities strengthen the well-known convolution inequality for the Fisher information as well as the entropy power inequality in dimensions $d>1$, while they reduce to the former in $d=1$. Our results recover the original Bergström inequality and generalize a proof of Bergström's inequality given by Dembo, Cover and Thomas. We characterize the equality case in our entropic Bonnesen inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropic versions of Bergström's and Bonnesen's inequalities Fradelizi, Matthieu Gavalakis, Lampros Rapaport, Martin Information Theory Functional Analysis 52A40, 94A17 We establish analogues of the Bergström and Bonnesen inequalities, related to determinants and volumes respectively, for the entropy power and for the Fisher information. The obtained inequalities strengthen the well-known convolution inequality for the Fisher information as well as the entropy power inequality in dimensions $d>1$, while they reduce to the former in $d=1$. Our results recover the original Bergström inequality and generalize a proof of Bergström's inequality given by Dembo, Cover and Thomas. We characterize the equality case in our entropic Bonnesen inequality. |
| title | Entropic versions of Bergström's and Bonnesen's inequalities |
| topic | Information Theory Functional Analysis 52A40, 94A17 |
| url | https://arxiv.org/abs/2501.10309 |