Entropy and Information jump for log-concave vectors
We extend the result of Ball and Nguyen on the jump of entropy under convolution for log-concave random vectors. We show that the result holds for any pair of vectors (not necessarily identically distributed) and that a similar inequality holds for the Fisher information, thus providing a quantitati...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-02-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.390/ |
| _version_ | 1797651501564297216 |
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| author | Bizeul, Pierre |
| author_facet | Bizeul, Pierre |
| author_sort | Bizeul, Pierre |
| collection | DOAJ |
| description | We extend the result of Ball and Nguyen on the jump of entropy under convolution for log-concave random vectors. We show that the result holds for any pair of vectors (not necessarily identically distributed) and that a similar inequality holds for the Fisher information, thus providing a quantitative Blachmann–Stam inequality. |
| first_indexed | 2024-03-11T16:16:43Z |
| format | Article |
| id | doaj.art-da69fd9203bd449eba7b2cd146dd9489 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:43Z |
| publishDate | 2023-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-da69fd9203bd449eba7b2cd146dd94892023-10-24T14:20:17ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-02-01361G248749310.5802/crmath.39010.5802/crmath.390Entropy and Information jump for log-concave vectorsBizeul, Pierre0Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université, 4 place de Jussieu 75005 Paris, FranceWe extend the result of Ball and Nguyen on the jump of entropy under convolution for log-concave random vectors. We show that the result holds for any pair of vectors (not necessarily identically distributed) and that a similar inequality holds for the Fisher information, thus providing a quantitative Blachmann–Stam inequality.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.390/ |
| spellingShingle | Bizeul, Pierre Entropy and Information jump for log-concave vectors Comptes Rendus. Mathématique |
| title | Entropy and Information jump for log-concave vectors |
| title_full | Entropy and Information jump for log-concave vectors |
| title_fullStr | Entropy and Information jump for log-concave vectors |
| title_full_unstemmed | Entropy and Information jump for log-concave vectors |
| title_short | Entropy and Information jump for log-concave vectors |
| title_sort | entropy and information jump for log concave vectors |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.390/ |
| work_keys_str_mv | AT bizeulpierre entropyandinformationjumpforlogconcavevectors |