RANDOM PERMUTATIONS WITH CYCLE WEIGHTS

• 成果类型: Article
• 署名作者: Betz, Volker; Ueltschi, Daniel; Velenik, Yvan
• 署名单位: University of Warwick; University of Geneva
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP697
• 发表日期: 2011
• 页码: 312-331
• 关键词: random partitions; brownian-motion

摘要

We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number n of elements, or a fraction of n or a logarithmic power of n.