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Precise Deviations for the Ewens-Pitman Model
Zhiqi Peng, Youzhou Zhou · 2025-12-13 · via math.PR updates on arXiv.org

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 $α=\frac{1}{2}$.

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