The order of large random permutations with cycle weights

Storm, Julia and Zeindler, Dirk (2015) The order of large random permutations with cycle weights. Electronic Journal of Probability, 20: 126. ISSN 1083-6489

[thumbnail of 1b-StoZei_2015_05_15]
Preview
PDF (1b-StoZei_2015_05_15)
1b_StoZei_2015_05_15.pdf - Submitted Version

Download (700kB)
[thumbnail of 4331-23839-1-PB]
Preview
PDF (4331-23839-1-PB)
4331_23839_1_PB.pdf - Published Version
Available under License Creative Commons Attribution.

Download (675kB)

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 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.

Item Type:
Journal Article
Journal or Publication Title:
Electronic Journal of Probability
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
?? random permutationorder of a permutationlarge deviationslocal limit theoremstatistics and probabilitystatistics, probability and uncertainty ??
ID Code:
73885
Deposited By:
Deposited On:
25 Feb 2016 13:26
Refereed?:
No
Published?:
Published
Last Modified:
01 Oct 2024 00:10