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Random permutations with logarithmic cycle weights

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Random permutations with logarithmic cycle weights. / Robles, N.; Zeindler, D.
In: Annales de l'institut Henri Poincare (B) Probability and Statistics, Vol. 56, No. 3, 01.10.2020, p. 1991-2016.

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

Harvard

Robles, N & Zeindler, D 2020, 'Random permutations with logarithmic cycle weights', Annales de l'institut Henri Poincare (B) Probability and Statistics, vol. 56, no. 3, pp. 1991-2016. https://doi.org/10.1214/19-AIHP1025

APA

Robles, N., & Zeindler, D. (2020). Random permutations with logarithmic cycle weights. Annales de l'institut Henri Poincare (B) Probability and Statistics, 56(3), 1991-2016. https://doi.org/10.1214/19-AIHP1025

Vancouver

Robles N, Zeindler D. Random permutations with logarithmic cycle weights. Annales de l'institut Henri Poincare (B) Probability and Statistics. 2020 Oct 1;56(3):1991-2016. Epub 2020 Jun 26. doi: 10.1214/19-AIHP1025

Author

Robles, N. ; Zeindler, D. / Random permutations with logarithmic cycle weights. In: Annales de l'institut Henri Poincare (B) Probability and Statistics. 2020 ; Vol. 56, No. 3. pp. 1991-2016.

Bibtex

@article{f9e8424717f44628ad652c8df4a7b513,
title = "Random permutations with logarithmic cycle weights",
abstract = "We consider random permutations on Sn with logarithmic growing cycles weights and study the asymptotic behavior as the length n tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables and also compute the total variation distance between both processes. Next, we prove a central limit theorem for the total number of cycles. Furthermore we establish a shape theorem and a functional central limit theorem for the Young diagrams associated to random permutations under this measure. We prove these results using tools from complex analysis and combinatorics. In particular we have to apply the method of singularity analysis to generating functions of the form exp((− log(1 − z))k+1) with k ≥ 1, which have not yet been studied in the literature. ",
keywords = "Cycle counts, Functional central limit theorem, Limit shape, Random permutations, Singularity analysis, Tauberian theorem, Total number of cycles, Total variation distance",
author = "N. Robles and D. Zeindler",
year = "2020",
month = oct,
day = "1",
doi = "10.1214/19-AIHP1025",
language = "English",
volume = "56",
pages = "1991--2016",
journal = "Annales de l'institut Henri Poincare (B) Probability and Statistics",
issn = "0246-0203",
publisher = "Institute of Mathematical Statistics",
number = "3",

}

RIS

TY - JOUR

T1 - Random permutations with logarithmic cycle weights

AU - Robles, N.

AU - Zeindler, D.

PY - 2020/10/1

Y1 - 2020/10/1

N2 - We consider random permutations on Sn with logarithmic growing cycles weights and study the asymptotic behavior as the length n tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables and also compute the total variation distance between both processes. Next, we prove a central limit theorem for the total number of cycles. Furthermore we establish a shape theorem and a functional central limit theorem for the Young diagrams associated to random permutations under this measure. We prove these results using tools from complex analysis and combinatorics. In particular we have to apply the method of singularity analysis to generating functions of the form exp((− log(1 − z))k+1) with k ≥ 1, which have not yet been studied in the literature.

AB - We consider random permutations on Sn with logarithmic growing cycles weights and study the asymptotic behavior as the length n tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables and also compute the total variation distance between both processes. Next, we prove a central limit theorem for the total number of cycles. Furthermore we establish a shape theorem and a functional central limit theorem for the Young diagrams associated to random permutations under this measure. We prove these results using tools from complex analysis and combinatorics. In particular we have to apply the method of singularity analysis to generating functions of the form exp((− log(1 − z))k+1) with k ≥ 1, which have not yet been studied in the literature.

KW - Cycle counts

KW - Functional central limit theorem

KW - Limit shape

KW - Random permutations

KW - Singularity analysis

KW - Tauberian theorem

KW - Total number of cycles

KW - Total variation distance

U2 - 10.1214/19-AIHP1025

DO - 10.1214/19-AIHP1025

M3 - Journal article

VL - 56

SP - 1991

EP - 2016

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

SN - 0246-0203

IS - 3

ER -