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

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  • Galganov, Oleksii
  • Ilienko, Andrii

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.

Suggested Citation

  • Galganov, Oleksii & Ilienko, Andrii, 2024. "Short cycles of random permutations with cycle weights: Point processes approach," Statistics & Probability Letters, Elsevier, vol. 213(C).
    • Handle: RePEc:eee:stapro:v:213:y:2024:i:c:s016771522400138x
    DOI: 10.1016/j.spl.2024.110169
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    References listed on IDEAS

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    1. Liu, Yang, 2020. "A general treatment of alternative expectation formulae," Statistics & Probability Letters, Elsevier, vol. 166(C).
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