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Random permutations without macroscopic cycles

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Random permutations without macroscopic cycles. / Betz, Volker; Schäfer, Helge; Zeindler, Dirk.
In: Annals of Applied Probability, Vol. 30, No. 3, 01.06.2020, p. 1484-1505.

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

Harvard

Betz, V, Schäfer, H & Zeindler, D 2020, 'Random permutations without macroscopic cycles', Annals of Applied Probability, vol. 30, no. 3, pp. 1484-1505. https://doi.org/10.1214/19-AAP1538

APA

Betz, V., Schäfer, H., & Zeindler, D. (2020). Random permutations without macroscopic cycles. Annals of Applied Probability, 30(3), 1484-1505. https://doi.org/10.1214/19-AAP1538

Vancouver

Betz V, Schäfer H, Zeindler D. Random permutations without macroscopic cycles. Annals of Applied Probability. 2020 Jun 1;30(3):1484-1505. doi: 10.1214/19-AAP1538

Author

Betz, Volker ; Schäfer, Helge ; Zeindler, Dirk. / Random permutations without macroscopic cycles. In: Annals of Applied Probability. 2020 ; Vol. 30, No. 3. pp. 1484-1505.

Bibtex

@article{9008525f0fcc46ce84fca8a0bc0da027,
title = "Random permutations without macroscopic cycles",
abstract = "We consider uniform random permutations of length n conditioned to have no cyclelonger than nβ with 0 < β < 1, in the limit of large n. Since in unconstrained uniform random permutations most of the indices are in cycles of macroscopic length, this is a singular conditioning in the limit. Nevertheless, we obtain a fairly complete picture about the cycle number distribution at various lengths. Depending on the scale at which cycle numbers are studied, our results include Poisson convergence, a central limit theorem, a shape theorem and two different functional central limit theorems.",
author = "Volker Betz and Helge Sch{\"a}fer and Dirk Zeindler",
year = "2020",
month = jun,
day = "1",
doi = "10.1214/19-AAP1538",
language = "English",
volume = "30",
pages = "1484--1505",
journal = "Annals of Applied Probability",
issn = "1050-5164",
publisher = "Institute of Mathematical Statistics",
number = "3",

}

RIS

TY - JOUR

T1 - Random permutations without macroscopic cycles

AU - Betz, Volker

AU - Schäfer, Helge

AU - Zeindler, Dirk

PY - 2020/6/1

Y1 - 2020/6/1

N2 - We consider uniform random permutations of length n conditioned to have no cyclelonger than nβ with 0 < β < 1, in the limit of large n. Since in unconstrained uniform random permutations most of the indices are in cycles of macroscopic length, this is a singular conditioning in the limit. Nevertheless, we obtain a fairly complete picture about the cycle number distribution at various lengths. Depending on the scale at which cycle numbers are studied, our results include Poisson convergence, a central limit theorem, a shape theorem and two different functional central limit theorems.

AB - We consider uniform random permutations of length n conditioned to have no cyclelonger than nβ with 0 < β < 1, in the limit of large n. Since in unconstrained uniform random permutations most of the indices are in cycles of macroscopic length, this is a singular conditioning in the limit. Nevertheless, we obtain a fairly complete picture about the cycle number distribution at various lengths. Depending on the scale at which cycle numbers are studied, our results include Poisson convergence, a central limit theorem, a shape theorem and two different functional central limit theorems.

U2 - 10.1214/19-AAP1538

DO - 10.1214/19-AAP1538

M3 - Journal article

VL - 30

SP - 1484

EP - 1505

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 3

ER -