Second-order limits for component counts C_{j_n}(n) in Chinese restaurant process partitions are a stationary Ornstein-Uhlenbeck process in the subcritical regime and a stationary M/M/∞ queue in the critical regime, obtained by first proving the results for the Karlin infinite urn model.
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2026 2verdicts
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A quenched functional central limit theorem is proved for component counts in Ewens-Pitman partitions, showing fluctuations split into two conditionally independent sources given alpha-diversity.
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Second-order fluctuations for a phase transition in random partitions
Second-order limits for component counts C_{j_n}(n) in Chinese restaurant process partitions are a stationary Ornstein-Uhlenbeck process in the subcritical regime and a stationary M/M/∞ queue in the critical regime, obtained by first proving the results for the Karlin infinite urn model.
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On central limit theorems for Ewens-Pitman model
A quenched functional central limit theorem is proved for component counts in Ewens-Pitman partitions, showing fluctuations split into two conditionally independent sources given alpha-diversity.