{"ID":2829553,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.12323","arxiv_id":"2512.12323","title":"Precise Deviations for the Ewens-Pitman Model","abstract":"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 $α=\\frac{1}{2}$.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2512.12323","url_pdf":"https://arxiv.org/pdf/2512.12323v1","authors":"[\"Zhiqi Peng\",\"Youzhou Zhou\"]","published":"2025-12-13T13:30:08Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}