Records in the Infinite Occupancy Scheme
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910696095088640 |
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| author | Derbazi, Zakaria Gnedin, Alexander Marynych, Alexander |
| author_facet | Derbazi, Zakaria Gnedin, Alexander Marynych, Alexander |
| contents | We consider the classic infinite occupancy scheme, where balls are thrown in boxes independently, with probability $p_j$ of hitting box $j$. Each time a box receives its first ball we speak of a record and, more generally, call an $r$-record every event when a box receives its $r$th ball. Assuming that the sequence $(p_j)$ is not decaying too fast, we show that after many balls have been thrown, the suitably scaled point process of $r$-record times is approximately Poisson. The joint convergence of $r$-record processes is argued under a condition of regular variation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01739 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Records in the Infinite Occupancy Scheme Derbazi, Zakaria Gnedin, Alexander Marynych, Alexander Probability Primary: 60C05, secondary: 60F05, 60G55 We consider the classic infinite occupancy scheme, where balls are thrown in boxes independently, with probability $p_j$ of hitting box $j$. Each time a box receives its first ball we speak of a record and, more generally, call an $r$-record every event when a box receives its $r$th ball. Assuming that the sequence $(p_j)$ is not decaying too fast, we show that after many balls have been thrown, the suitably scaled point process of $r$-record times is approximately Poisson. The joint convergence of $r$-record processes is argued under a condition of regular variation. |
| title | Records in the Infinite Occupancy Scheme |
| topic | Probability Primary: 60C05, secondary: 60F05, 60G55 |
| url | https://arxiv.org/abs/2308.01739 |