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. ISSN 1083-6489

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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/1800/1804
Subjects:
ID Code:
73885
Deposited By:
Deposited On:
25 Feb 2016 13:26
Refereed?:
No
Published?:
Published
Last Modified:
24 Nov 2020 03:18