Year: 2025
Type: preprint
Abstract: We investigate the asymptotic behavior of the number of parts $K_n$ in the Ewens--Pitman partition model under the regime where the diversity parameter is scaled linearly with the sample size, that is, $\theta = \lambda n$ for some~$\lambda > 0$. While recent work has established a law of large numbers (LLN) and a central limit theorem (CLT) for $K_n$ in this regime, we revisit these results through a martingale-based approach. Our method yields significantly shorter proofs, and leads to sharper convergence rates in the CLT, including improved Berry--Esseen bounds in the case $\alpha = 0$, and a new result for the regime $\alpha \in (0,1)$, filling a gap in the literature.
Source: arXiv (Cornell University)
Author: Ribeiro, Rodrigo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979354582
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