Cycle length distributions in random permutations with diverging cycle weights

被引：6

作者：

Dereich, Steffen ^{[1
]}

Moerters, Peter ^{[2
]}

机构：

[1] Univ Munster, Inst Stat Math, D-48149 Munster, Germany

[2] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

来源：

RANDOM STRUCTURES & ALGORITHMS | 2015年 / 46卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

random permutations; random partitions; Bose-Einstein condensation; cycle structure; cycle weights; generalised Ewens distribution; gamma distribution; condensing wave; local limit theorem;

D O I：

10.1002/rsa.20520

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We study the model of random permutations with diverging cycle weights, which was recently considered by Ercolani and Ueltschi, and others. Assuming only regular variation of the cycle weights we obtain a very precise local limit theorem for the size of a typical cycle, and use this to show that the empirical distribution of properly rescaled cycle lengths converges in probability to a gamma distribution.Copyright (c) 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46,635-650, 2015

引用

页码：635 / 650

页数：16

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