Minimum entropy of a log-concave variable for fixed variance
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917614816591872 |
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| author | Melbourne, James Nayar, Piotr Roberto, Cyril |
| author_facet | Melbourne, James Nayar, Piotr Roberto, Cyril |
| contents | We show that for log-concave real random variables with fixed variance the Shannon differential entropy is minimized for an exponential random variable. We apply this result to derive upper bounds on capacities of additive noise channels with log-concave noise. We also improve constants in the reverse entropy power inequalities for log-concave random variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01840 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimum entropy of a log-concave variable for fixed variance Melbourne, James Nayar, Piotr Roberto, Cyril Probability Information Theory We show that for log-concave real random variables with fixed variance the Shannon differential entropy is minimized for an exponential random variable. We apply this result to derive upper bounds on capacities of additive noise channels with log-concave noise. We also improve constants in the reverse entropy power inequalities for log-concave random variables. |
| title | Minimum entropy of a log-concave variable for fixed variance |
| topic | Probability Information Theory |
| url | https://arxiv.org/abs/2309.01840 |