CENTRAL LIMIT THEOREMS FOR PATTERNS IN MULTISET PERMUTATIONS AND SET PARTITIONS

• 成果类型: Article
• 署名作者: Feray, Valentin
• 署名单位: University of Zurich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1502
• 发表日期: 2020
• 页码: 287-323
• 关键词: probability; number; occurrences; statistics; BEHAVIOR; sums

摘要

We use the recently developed method of weighted dependency graphs to prove central limit theorems for the number of occurrences of any fixed pattern in multiset permutations and in set partitions. This generalizes results for patterns of size 2 in both settings, obtained by Canfield, Janson and Zeil-berger and Chern, Diaconis, Kane and Rhoades, respectively.