RANDOM PERMUTATIONS WITH CYCLE WEIGHTS

被引：36

作者：

Betz, Volker ^{[1
]}

Ueltschi, Daniel ^{[1
]}

Velenik, Yvan ^{[2
]}

机构：

[1] Univ Warwick, Dept Math, Coventry CV4 7AL, W Midlands, England

[2] Univ Geneva, Sect Math, CH-1211 Geneva 4, Switzerland

来源：

ANNALS OF APPLIED PROBABILITY | 2011年 / 21卷 / 01期

基金：

美国国家科学基金会; 瑞士国家科学基金会; 英国工程与自然科学研究理事会;

关键词：

Random permutations; cycle weights; cycle lengths; Ewens distribution; RANDOM PARTITIONS; BROWNIAN-MOTION;

D O I：

10.1214/10-AAP697

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：312 / 331

页数：20

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