Scaling limit for small blocks in the Chinese restaurant process
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866908581500026880 |
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| author | Galganov, Oleksii Ilienko, Andrii |
| author_facet | Galganov, Oleksii Ilienko, Andrii |
| contents | The Chinese restaurant process is a basic sequential construction of consistent random partitions. We consider random point measures describing the composition of small blocks in such partitions and show that their scaling limit is given by the projective limit of certain inhomogeneous Poisson measures on cones of increasing dimension. This result makes it possible to derive classical and functional limit theorems in the Skorokhod topology for various characteristics of the Chinese restaurant process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05578 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling limit for small blocks in the Chinese restaurant process Galganov, Oleksii Ilienko, Andrii Probability 60C05, 60G55 (Primary) 60F17 (Secondary) The Chinese restaurant process is a basic sequential construction of consistent random partitions. We consider random point measures describing the composition of small blocks in such partitions and show that their scaling limit is given by the projective limit of certain inhomogeneous Poisson measures on cones of increasing dimension. This result makes it possible to derive classical and functional limit theorems in the Skorokhod topology for various characteristics of the Chinese restaurant process. |
| title | Scaling limit for small blocks in the Chinese restaurant process |
| topic | Probability 60C05, 60G55 (Primary) 60F17 (Secondary) |
| url | https://arxiv.org/abs/2502.05578 |