随机排列中下降数的锐大偏差和集中不等式

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY Journal of Applied Probability Pub Date : 2024-01-05 DOI:10.1017/jpr.2023.86

Bernard Bercu, Michel Bonnefont, Adrien Richou

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引用次数: 0

摘要

本文的目标是进一步分析随机排列中的下降数的行为。通过两种不同的方法，即依靠合适的马氏分解或欧文-霍尔分布，我们证明了下降数满足一个尖锐的大偏差原理。我们还提供了一个非常精确的集中不等式，涉及大偏差原理中的速率函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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-deviation principle. A very precise concentration inequality involving the rate function in the large-deviation principle is also provided.

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来源期刊

Journal of Applied Probability 数学-统计学与概率论

CiteScore

1.50

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.