Cycle length distributions in random permutations with diverging cycle weights

Steffen Dereich; Peter Morters

doi:10.1002/rsa.20520

Cycle length distributions in random permutations with diverging cycle weights

Steffen Dereich, Peter Morters

University of Münster

Research output: Contribution to journal › Article › peer-review

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Abstract

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.

Original language	English
Pages (from-to)	635-650
Journal	Random Structures and Algorithms
Volume	46
Issue number	4
Early online date	30 Oct 2013
DOIs	https://doi.org/10.1002/rsa.20520
Publication status	Published - 1 May 2015

Keywords

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

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10.1002/rsa.20520

Dereich_et_al-2015-Random_Structures_&_AlgorithmsFinal published version, 140 KBLicence: CC BY

Cite this

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KW - Random permutations

KW - local limit theorem

KW - condensing wave

KW - gamma distribution

KW - generalised Ewens distribution

KW - cycle weights

KW - cycle structure

KW - Bose-Einstein condensation

KW - random partitions

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Cycle length distributions in random permutations with diverging cycle weights

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Keywords

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Emergence of Condensation in Stochastic Systems

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Cycle length distributions in random permutations with diverging cycle weights

Abstract

Keywords

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Emergence of Condensation in Stochastic Systems

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