Bernoulli sums and Rényi entropy inequalities
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909138068439040 |
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| author | Madiman, Mokshay Melbourne, James Roberto, Cyril |
| author_facet | Madiman, Mokshay Melbourne, James Roberto, Cyril |
| contents | We investigate the Rényi entropy of independent sums of integer valued random variables through Fourier theoretic means, and give sharp comparisons between the variance and the Rényi entropy, for Poisson-Bernoulli variables. As applications we prove that a discrete ``min-entropy power'' is super additive on independent variables up to a universal constant, and give new bounds on an entropic generalization of the Littlewood-Offord problem that are sharp in the ``Poisson regime''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_00896 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Bernoulli sums and Rényi entropy inequalities Madiman, Mokshay Melbourne, James Roberto, Cyril Probability Information Theory Combinatorics We investigate the Rényi entropy of independent sums of integer valued random variables through Fourier theoretic means, and give sharp comparisons between the variance and the Rényi entropy, for Poisson-Bernoulli variables. As applications we prove that a discrete ``min-entropy power'' is super additive on independent variables up to a universal constant, and give new bounds on an entropic generalization of the Littlewood-Offord problem that are sharp in the ``Poisson regime''. |
| title | Bernoulli sums and Rényi entropy inequalities |
| topic | Probability Information Theory Combinatorics |
| url | https://arxiv.org/abs/2103.00896 |