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Moderate deviations for the number of descents in a random permutation

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  • Jiang, Hui
  • Wang, Jing

Abstract

The number of descents in a random permutation has close connections with generalized Pólya urn and random trees. Via the Laplace functional calculations and asymptotic analysis techniques, we prove that the number of descents satisfies the moderate deviations and Cramér type moderate deviations. Then, using the martingale difference representation, we establish the functional moderate deviations in D([0,1],R) equipped with the uniform topology.

Suggested Citation

  • Jiang, Hui & Wang, Jing, 2025. "Moderate deviations for the number of descents in a random permutation," Statistics & Probability Letters, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:stapro:v:219:y:2025:i:c:s016771522400289x
    DOI: 10.1016/j.spl.2024.110320
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    References listed on IDEAS

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    1. Puhalskii, A., 1994. "The method of stochastic exponentials for large deviations," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 45-70, November.
    2. Sourav Chatterjee & Persi Diaconis, 2017. "A central limit theorem for a new statistic on permutations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 48(4), pages 561-573, December.
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