Precise Deviations for the Ewens-Pitman Model
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909959998930944 |
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| author | Peng, Zhiqi Zhou, Youzhou |
| author_facet | Peng, Zhiqi Zhou, Youzhou |
| contents | In this paper, we derive an integral representation for the distribution of the number of types $K_n$ in the Ewens-Pitman model. Based on this representation, we also establish precise large deviations and precise moderate deviations for $K_n$. After careful examination, we find that the rate function exhibits a second-order phase transition and the critical point is $α=\frac{1}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Precise Deviations for the Ewens-Pitman Model Peng, Zhiqi Zhou, Youzhou Probability Statistics Theory Primary 60F10, secondary 60G57 In this paper, we derive an integral representation for the distribution of the number of types $K_n$ in the Ewens-Pitman model. Based on this representation, we also establish precise large deviations and precise moderate deviations for $K_n$. After careful examination, we find that the rate function exhibits a second-order phase transition and the critical point is $α=\frac{1}{2}$. |
| title | Precise Deviations for the Ewens-Pitman Model |
| topic | Probability Statistics Theory Primary 60F10, secondary 60G57 |
| url | https://arxiv.org/abs/2512.12323 |