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Large cycles and a functional central limit theorem for generalized weighted random permutations

Research output: Contribution to Journal/Magazine › Journal article

Unpublished

Standard

Large cycles and a functional central limit theorem for generalized weighted random permutations. / Nikeghbali, Ashkan; Storm, Julia; Zeindler, Dirk.
In: arxiv.org, 2013.

Research output: Contribution to Journal/Magazine › Journal article

Harvard

Nikeghbali, A, Storm, J & Zeindler, D 2013, 'Large cycles and a functional central limit theorem for generalized weighted random permutations', arxiv.org. <http://arxiv.org/abs/1302.5938>

APA

Nikeghbali, A., Storm, J., & Zeindler, D. (2013). Large cycles and a functional central limit theorem for generalized weighted random permutations. Unpublished. http://arxiv.org/abs/1302.5938

Vancouver

Nikeghbali A, Storm J, Zeindler D. Large cycles and a functional central limit theorem for generalized weighted random permutations. arxiv.org. 2013.

Author

Nikeghbali, Ashkan ; Storm, Julia ; Zeindler, Dirk. / Large cycles and a functional central limit theorem for generalized weighted random permutations. In: arxiv.org. 2013.

Bibtex

@article{b378194ba8ad420899bd5fd4858ef1da,
title = "Large cycles and a functional central limit theorem for generalized weighted random permutations",
abstract = "The objects of our interest are the so-called A-permutations, which are permutations whose cycle length lie in a fixed set A. They have been extensively studied with respect to the uniform or the Ewens measure. In this paper, we extend some classical results to a more general weighted probability measure which is a natural extension of the Ewens measure and which in particular allows to consider sets An depending on the degree n of the permutation. By means of complex analysis arguments and under reasonable conditions on generating functions we study the asymptotic behaviour of classical statistics. More precisely, we generalize results concerning large cycles of random permutations by Vershik, Shmidt and Kingman, namely the weak convergence of the size ordered cycle length to a Poisson-Dirichlet distribution. Furthermore, we apply our tools to the cycle counts and obtain a Brownian motion central limit theorem which extends results by DeLaurentis, Pittel and Hansen.",
author = "Ashkan Nikeghbali and Julia Storm and Dirk Zeindler",
note = "Preprint",
year = "2013",
language = "English",
journal = "arxiv.org",

}

RIS

TY - JOUR

T1 - Large cycles and a functional central limit theorem for generalized weighted random permutations

AU - Nikeghbali, Ashkan

AU - Storm, Julia

AU - Zeindler, Dirk

N1 - Preprint

PY - 2013

Y1 - 2013

N2 - The objects of our interest are the so-called A-permutations, which are permutations whose cycle length lie in a fixed set A. They have been extensively studied with respect to the uniform or the Ewens measure. In this paper, we extend some classical results to a more general weighted probability measure which is a natural extension of the Ewens measure and which in particular allows to consider sets An depending on the degree n of the permutation. By means of complex analysis arguments and under reasonable conditions on generating functions we study the asymptotic behaviour of classical statistics. More precisely, we generalize results concerning large cycles of random permutations by Vershik, Shmidt and Kingman, namely the weak convergence of the size ordered cycle length to a Poisson-Dirichlet distribution. Furthermore, we apply our tools to the cycle counts and obtain a Brownian motion central limit theorem which extends results by DeLaurentis, Pittel and Hansen.

AB - The objects of our interest are the so-called A-permutations, which are permutations whose cycle length lie in a fixed set A. They have been extensively studied with respect to the uniform or the Ewens measure. In this paper, we extend some classical results to a more general weighted probability measure which is a natural extension of the Ewens measure and which in particular allows to consider sets An depending on the degree n of the permutation. By means of complex analysis arguments and under reasonable conditions on generating functions we study the asymptotic behaviour of classical statistics. More precisely, we generalize results concerning large cycles of random permutations by Vershik, Shmidt and Kingman, namely the weak convergence of the size ordered cycle length to a Poisson-Dirichlet distribution. Furthermore, we apply our tools to the cycle counts and obtain a Brownian motion central limit theorem which extends results by DeLaurentis, Pittel and Hansen.

M3 - Journal article

JO - arxiv.org

JF - arxiv.org

ER -