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 $\hat{I}\pm =\frac{1}{2}$.

17 pages, 1 figure