- 1b-StoZei_2015_05_15
Submitted manuscript, 684 KB, PDF document

- 4331-23839-1-PB
Final published version, 659 KB, PDF document

Available under license: CC BY: Creative Commons Attribution 4.0 International License

- http://ejp.ejpecp.org/article/view/4331
Final published version

Research output: Contribution to journal › Journal article

Published

**The order of large random permutations with cycle weights.** / Storm, Julia; Zeindler, Dirk.

Research output: Contribution to journal › Journal article

Storm, J & Zeindler, D 2015, 'The order of large random permutations with cycle weights', *Electronic Journal of Probability*, vol. 20, 126. https://doi.org/10.1214/EJP.v20-4331

Storm, J., & Zeindler, D. (2015). The order of large random permutations with cycle weights. *Electronic Journal of Probability*, *20*, [126]. https://doi.org/10.1214/EJP.v20-4331

Storm J, Zeindler D. The order of large random permutations with cycle weights. Electronic Journal of Probability. 2015 Dec 5;20. 126. https://doi.org/10.1214/EJP.v20-4331

@article{580399a04fee401792acdd70196c6c4d,

title = "The order of large random permutations with cycle weights",

abstract = "The order On(σ) of a permutation σ of n objects is the smallest integer k≥1 such that the k-th iterate of σ gives the identity. A remarkable result about the order of a uniformly chosen permutation is due to Erd{\"o}s and Tur{\'a}n who proved in 1965 that logOn satisfies a central limit theorem. We extend this result to the so-called generalized Ewens measure in a previous paper. In this paper, we establish a local limit theorem as well as, under some extra moment condition, a precise large deviations estimate. These properties are new even for the uniform measure. Furthermore, we provide precise large deviations estimates for random permutations with polynomial cycle weights.",

keywords = "random permutation, order of a permutation, large deviations, local limit theorem",

author = "Julia Storm and Dirk Zeindler",

year = "2015",

month = dec,

day = "5",

doi = "10.1214/EJP.v20-4331",

language = "English",

volume = "20",

journal = "Electronic Journal of Probability",

issn = "1083-6489",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - The order of large random permutations with cycle weights

AU - Storm, Julia

AU - Zeindler, Dirk

PY - 2015/12/5

Y1 - 2015/12/5

N2 - The order On(σ) of a permutation σ of n objects is the smallest integer k≥1 such that the k-th iterate of σ gives the identity. A remarkable result about the order of a uniformly chosen permutation is due to Erdös and Turán who proved in 1965 that logOn satisfies a central limit theorem. We extend this result to the so-called generalized Ewens measure in a previous paper. In this paper, we establish a local limit theorem as well as, under some extra moment condition, a precise large deviations estimate. These properties are new even for the uniform measure. Furthermore, we provide precise large deviations estimates for random permutations with polynomial cycle weights.

AB - The order On(σ) of a permutation σ of n objects is the smallest integer k≥1 such that the k-th iterate of σ gives the identity. A remarkable result about the order of a uniformly chosen permutation is due to Erdös and Turán who proved in 1965 that logOn satisfies a central limit theorem. We extend this result to the so-called generalized Ewens measure in a previous paper. In this paper, we establish a local limit theorem as well as, under some extra moment condition, a precise large deviations estimate. These properties are new even for the uniform measure. Furthermore, we provide precise large deviations estimates for random permutations with polynomial cycle weights.

KW - random permutation

KW - order of a permutation

KW - large deviations

KW - local limit theorem

U2 - 10.1214/EJP.v20-4331

DO - 10.1214/EJP.v20-4331

M3 - Journal article

VL - 20

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

SN - 1083-6489

M1 - 126

ER -