Short cycles of random permutations with cycle weights: Point processes approach

Oleksii Galganov and Andrii Ilienko

Statistics & Probability Letters, 2024, vol. 213, issue C

Abstract: We study the asymptotic behavior of short cycles of random permutations with cycle weights. More specifically, on a specially constructed metric space whose elements encode all possible cycles, we consider a point process containing all information on cycles of a given random permutation on {1,…,n}. The main result of the paper is the distributional convergence with respect to the vague topology of the above processes towards a Poisson point process as n→∞ for a wide range of cycle weights. As an application, we give several limit theorems for various statistics of cycles.

Keywords: Random permutation; Cycle structure; Point process; Poisson convergence (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110169

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