SHARP ANALYSIS ON THE JOINT DISTRIBUTION OF THE NUMBER OF DESCENTS AND INVERSE DESCENTS IN A RANDOM PERMUTATION
成果类型：
Article
署名作者：
Bercu, Bernard; Bonnefont, Michel; Fredes, Luis; Richou, Adrien
署名单位：
Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bordeaux
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/24-AAP2138
发表日期：
2025
页码：
1143-1163
关键词：
摘要：
Chatterjee and Diaconis have recently shown the asymptotic normality for the joint distribution of the number of descents and inverse descents in a random permutation. A noteworthy point of their results is that the asymptotic variance of the normal distribution is diagonal, which means that the number of descents and inverse descents are asymptotically uncorrelated. The goal of this paper is to go further in this analysis by proving a large deviation principle for the joint distribution. We shall show that the rate function of the joint distribution is the sum of the rate functions of the marginal distributions, which also means that the number of descents and inverse descents are asymptotically independent at the large deviation level. However, we are going to prove that they are finely dependent at the sharp large deviation level.
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