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Article Dans Une Revue Journal of Applied Probability Année : 2024

Sharp large deviations and concentration inequalities for the number of descents in a random permutation

Bernard Bercu
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Michel Bonnefont
Adrien Richou

Résumé

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.
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Dates et versions

hal-03819631 , version 1 (18-10-2022)
hal-03819631 , version 2 (29-09-2023)

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Bernard Bercu, Michel Bonnefont, Adrien Richou. Sharp large deviations and concentration inequalities for the number of descents in a random permutation. Journal of Applied Probability, 2024, pp.1-24. ⟨10.1017/jpr.2023.86⟩. ⟨hal-03819631v2⟩

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