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

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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:
?? random permutationorder of a permutationlarge deviationslocal limit theoremstatistics and probabilitystatistics, probability and uncertainty ??
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Deposited On:
25 Feb 2016 13:26
Last Modified:
05 Feb 2024 00:35