Divisibility and primality in random walks
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914583710531584 |
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| author | Weber, Michel J. G. |
| author_facet | Weber, Michel J. G. |
| contents | In this paper we study the divisibility and primality properties of the Bernoulli random walk. We improve or extend some of our divisibility results to wide classes of iid or independent non iid random walks. We also obtain new primality results for the Rademacher random walk. We study the value distribution of divisors of the random walk in the Cramér model, and obtain a general estimate of a similar kind to that of the Bernouilli model. Earlier results on divisors and quasi-prime numbers in the Bernoulli model are recorded, as well as some other recent for the Cramér random model, based on an estimate due to Selberg. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14828 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Divisibility and primality in random walks Weber, Michel J. G. Probability Primary 11K65, 11N37, 60G50, Secondary 11A25, 60E05, 60F15 In this paper we study the divisibility and primality properties of the Bernoulli random walk. We improve or extend some of our divisibility results to wide classes of iid or independent non iid random walks. We also obtain new primality results for the Rademacher random walk. We study the value distribution of divisors of the random walk in the Cramér model, and obtain a general estimate of a similar kind to that of the Bernouilli model. Earlier results on divisors and quasi-prime numbers in the Bernoulli model are recorded, as well as some other recent for the Cramér random model, based on an estimate due to Selberg. |
| title | Divisibility and primality in random walks |
| topic | Probability Primary 11K65, 11N37, 60G50, Secondary 11A25, 60E05, 60F15 |
| url | https://arxiv.org/abs/2310.14828 |