Long cycle of random permutations with polynomially growing cycle weights

被引：0

作者：

Zeindler, Dirk ^{[1
]}

机构：

[1] Univ Lancaster, Dept Math & Stat, Fylde Coll, Bailrigg, England

来源：

RANDOM STRUCTURES & ALGORITHMS | 2021年 / 58卷 / 04期

关键词：

cycle counts; long cycles; Poisson process; random permutations; saddle point method; SAMPLING THEORY; NUMBER;

D O I：

10.1002/rsa.20989

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We study random permutations of n objects with respect to multiplicative measures with polynomial growing cycle weights. We determine in this paper the asymptotic behavior of the long cycles under this measure and also prove that the cumulative cycle numbers converge in the region of the long cycles to a Poisson process.

引用

页码：726 / 739

页数：14

共 21 条

[1] THE CYCLE STRUCTURE OF RANDOM PERMUTATIONS [J].

ARRATIA, R ;

TAVARE, S .

ANNALS OF PROBABILITY, 1992, 20 (03) :1567-1591

[2]

Arratia R., 2003, EMS Monographs in Mathematics

[3]

Betz V., 2017, RANDOM PERMUTATIONS

[4] RANDOM PERMUTATIONS WITH CYCLE WEIGHTS [J].

Betz, Volker ;

Ueltschi, Daniel ;

Velenik, Yvan .

ANNALS OF APPLIED PROBABILITY, 2011, 21 (01) :312-331

[5]

Billingsley P, 2013, CONVERGE PROBAB MEAS

[6]

Cipriani A, 2015, ALEA-LAT AM J PROBAB, V12, P971

[7] RANDOM PERMUTATIONS AND BROWNIAN-MOTION [J].

DELAURENTIS, JM ;

PITTEL, BG .

PACIFIC JOURNAL OF MATHEMATICS, 1985, 119 (02) :287-301

[8] Cycle length distributions in random permutations with diverging cycle weights [J].

Dereich, Steffen ;

Moerters, Peter .

RANDOM STRUCTURES & ALGORITHMS, 2015, 46 (04) :635-650

[9] Cycle Structure of Random Permutations With Cycle Weights [J].

Ercolani, Nicholas M. ;

Ueltschi, Daniel .

RANDOM STRUCTURES & ALGORITHMS, 2014, 44 (01) :109-133

[10] Limit shapes of Gibbs distributions on the set of integer partitions: The expansive case [J].

Erlihson, Michael M. ;

Granovsky, Boris L. .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2008, 44 (05) :915-945

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