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The generalized weighted probability measure on the symmetric group and the asymptotic behaviour of the cycles

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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The generalized weighted probability measure on the symmetric group and the asymptotic behaviour of the cycles. / Nikeghbali, Ashkan; Zeindler, Dirk.
In: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Vol. 49, No. 4, 2013, p. 961-981.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Nikeghbali, A & Zeindler, D 2013, 'The generalized weighted probability measure on the symmetric group and the asymptotic behaviour of the cycles', Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, vol. 49, no. 4, pp. 961-981. <http://projecteuclid.org/euclid.aihp/1380718733>

APA

Nikeghbali, A., & Zeindler, D. (2013). The generalized weighted probability measure on the symmetric group and the asymptotic behaviour of the cycles. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 49(4), 961-981. http://projecteuclid.org/euclid.aihp/1380718733

Vancouver

Nikeghbali A, Zeindler D. The generalized weighted probability measure on the symmetric group and the asymptotic behaviour of the cycles. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 2013;49(4):961-981.

Author

Nikeghbali, Ashkan ; Zeindler, Dirk. / The generalized weighted probability measure on the symmetric group and the asymptotic behaviour of the cycles. In: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 2013 ; Vol. 49, No. 4. pp. 961-981.

Bibtex

@article{b51806dfefac460bb9f075705cdb4b4f,
title = "The generalized weighted probability measure on the symmetric group and the asymptotic behaviour of the cycles",
abstract = "The goal of this paper is to analyse the asymptotic behaviour of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens measure. We combine tools from combinatorics and complex analysis (e.g. singularity analysis of generating functions) to prove that under some analytic conditions (on relevant generating functions) the cycle process converges to a vector of independent Poisson variables and to establish a central limit theorem for the total number of cycles. Our methods allow us to obtain an asymptotic estimate of the characteristic functions of the different random vectors of interest together with an error estimate, thus having a control on the speed of convergence. In fact we are able to prove a finer convergence for the total number of cycles, namely mod-Poisson convergence. From there we apply previous results on mod-Poisson convergence to obtain Poisson approximation for the total number of cycles as well as large deviations estimates.",
author = "Ashkan Nikeghbali and Dirk Zeindler",
year = "2013",
language = "English",
volume = "49",
pages = "961--981",
journal = "Annales de l'Institut Henri Poincar{\'e} (B) Probabilit{\'e}s et Statistiques",
issn = "0246-0203",
publisher = "Institute of Mathematical Statistics",
number = "4",

}

RIS

TY - JOUR

T1 - The generalized weighted probability measure on the symmetric group and the asymptotic behaviour of the cycles

AU - Nikeghbali, Ashkan

AU - Zeindler, Dirk

PY - 2013

Y1 - 2013

N2 - The goal of this paper is to analyse the asymptotic behaviour of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens measure. We combine tools from combinatorics and complex analysis (e.g. singularity analysis of generating functions) to prove that under some analytic conditions (on relevant generating functions) the cycle process converges to a vector of independent Poisson variables and to establish a central limit theorem for the total number of cycles. Our methods allow us to obtain an asymptotic estimate of the characteristic functions of the different random vectors of interest together with an error estimate, thus having a control on the speed of convergence. In fact we are able to prove a finer convergence for the total number of cycles, namely mod-Poisson convergence. From there we apply previous results on mod-Poisson convergence to obtain Poisson approximation for the total number of cycles as well as large deviations estimates.

AB - The goal of this paper is to analyse the asymptotic behaviour of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens measure. We combine tools from combinatorics and complex analysis (e.g. singularity analysis of generating functions) to prove that under some analytic conditions (on relevant generating functions) the cycle process converges to a vector of independent Poisson variables and to establish a central limit theorem for the total number of cycles. Our methods allow us to obtain an asymptotic estimate of the characteristic functions of the different random vectors of interest together with an error estimate, thus having a control on the speed of convergence. In fact we are able to prove a finer convergence for the total number of cycles, namely mod-Poisson convergence. From there we apply previous results on mod-Poisson convergence to obtain Poisson approximation for the total number of cycles as well as large deviations estimates.

M3 - Journal article

VL - 49

SP - 961

EP - 981

JO - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

JF - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

SN - 0246-0203

IS - 4

ER -