Short cycles of random permutations with cycle weights: point processes approach
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866913684080558080 |
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| author | Galganov, Oleksii Ilienko, Andrii |
| author_facet | Galganov, Oleksii Ilienko, Andrii |
| contents | 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 $\{1,\ldots,n\}$. 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 $n\to\infty$ for a wide range of cycle weights. As an application, we give several limit theorems for various statistics of cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10721 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Short cycles of random permutations with cycle weights: point processes approach Galganov, Oleksii Ilienko, Andrii Probability 60C05, 60G55 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 $\{1,\ldots,n\}$. 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 $n\to\infty$ for a wide range of cycle weights. As an application, we give several limit theorems for various statistics of cycles. |
| title | Short cycles of random permutations with cycle weights: point processes approach |
| topic | Probability 60C05, 60G55 |
| url | https://arxiv.org/abs/2309.10721 |