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

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-devia...

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Bibliographic Details
Published inJournal of applied probability Vol. 61; no. 3; pp. 810 - 833
Main Authors Bercu, Bernard, Bonnefont, Michel, Richou, Adrien
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2024
Cambridge University press
Subjects
Central limit theorem
Deviation
Inequality
Martingales
Mathematics
Original Article
Permutations
Probability
Random variables
random permutations
concentration inequalities
Large deviations
60F10
05A05
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2023.86