A stochastic process defined via the random permutation divisors
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918287038742528 |
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| author | Manstavičius, Eugenijus |
| author_facet | Manstavičius, Eugenijus |
| contents | The normalised partial sums of values of a nonnegative multiplicative function over divisors with appropriately restricted sizes of a random permutation from the symmetric group define trajectories of a stochastic process. We prove a functional limit theorem in the Skorokhod space when the permutations are drawn uniformly at random. Furthermore, we show that the paths of the limit process almost surely belong to the space of continuous functions on the unit interval and, exploiting the results from number-theoretical papers, we obtain rather complex formulas for the limits of joint power moments of the process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A stochastic process defined via the random permutation divisors Manstavičius, Eugenijus Probability 60F17, 60C05 The normalised partial sums of values of a nonnegative multiplicative function over divisors with appropriately restricted sizes of a random permutation from the symmetric group define trajectories of a stochastic process. We prove a functional limit theorem in the Skorokhod space when the permutations are drawn uniformly at random. Furthermore, we show that the paths of the limit process almost surely belong to the space of continuous functions on the unit interval and, exploiting the results from number-theoretical papers, we obtain rather complex formulas for the limits of joint power moments of the process. |
| title | A stochastic process defined via the random permutation divisors |
| topic | Probability 60F17, 60C05 |
| url | https://arxiv.org/abs/2501.10096 |