The Multinomial Allocation Model and the Random Box Load
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908994906357760 |
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| author | Sagitov, Serik |
| author_facet | Sagitov, Serik |
| contents | We revisit the random allocation model in which $n$ balls are independently placed into $N$ boxes with probabilities $q_1,\ldots,q_N$. A classical asymptotic result due to Kolchin, Sevastyanov, and Chistyakov for the expectations, variances, and covariances of the occupancy counts is reformulated in a compact and transparent form in terms of the load of a randomly selected box. We further derive explicit two-sided bounds for the associated remainder terms, obtained under weaker assumptions than those previously required. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15152 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Multinomial Allocation Model and the Random Box Load Sagitov, Serik Probability 60C05 We revisit the random allocation model in which $n$ balls are independently placed into $N$ boxes with probabilities $q_1,\ldots,q_N$. A classical asymptotic result due to Kolchin, Sevastyanov, and Chistyakov for the expectations, variances, and covariances of the occupancy counts is reformulated in a compact and transparent form in terms of the load of a randomly selected box. We further derive explicit two-sided bounds for the associated remainder terms, obtained under weaker assumptions than those previously required. |
| title | The Multinomial Allocation Model and the Random Box Load |
| topic | Probability 60C05 |
| url | https://arxiv.org/abs/2604.15152 |