Sharp large deviations and concentration inequalities for the number of descents in a random permutation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866915025285808128 |
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| author | Bercu, Bernard Bonnefont, Michel Richou, Adrien |
| author_facet | Bercu, Bernard Bonnefont, Michel Richou, Adrien |
| contents | The goal of this paper is to go further in the analysis of the behavior of the number of descents in a random permutation. Via two different approaches relying on a suitable martingale decomposition or on the Irwin-Hall distribution, we prove that the number of descents satisfies a sharp large deviation principle. A very precise concentration inequality involving the rate function in the large deviation principle is also provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_10382 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sharp large deviations and concentration inequalities for the number of descents in a random permutation Bercu, Bernard Bonnefont, Michel Richou, Adrien Probability The goal of this paper is to go further in the analysis of the behavior of the number of descents in a random permutation. Via two different approaches relying on a suitable martingale decomposition or on the Irwin-Hall distribution, we prove that the number of descents satisfies a sharp large deviation principle. A very precise concentration inequality involving the rate function in the large deviation principle is also provided. |
| title | Sharp large deviations and concentration inequalities for the number of descents in a random permutation |
| topic | Probability |
| url | https://arxiv.org/abs/2210.10382 |