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  • 1b-StoZei_2015_05_15

    Submitted manuscript, 684 KB, PDF document

  • 4331-23839-1-PB

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

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The order of large random permutations with cycle weights

Research output: Contribution to journalJournal article

Published
Article number126
<mark>Journal publication date</mark>5/12/2015
<mark>Journal</mark>Electronic Journal of Probability
Volume20
Number of pages34
Publication StatusPublished
<mark>Original language</mark>English

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.