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Sharp large deviations and concentration inequalities for the number of descents in a random permutation
Published online by Cambridge University Press: 05 January 2024
Abstract
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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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust