Scaling limit for small blocks in the Chinese restaurant process

Oleksii Galganov and Andrii Ilienko

Stochastic Processes and their Applications, 2026, vol. 192, issue C

Abstract: The Chinese restaurant process is a basic sequential construction of consistent random partitions. We consider random point measures describing the composition of small blocks in such partitions and show that their scaling limit is given by the projective limit of certain inhomogeneous Poisson measures on cones of increasing dimension. This result makes it possible to derive classical and functional limit theorems in the Skorokhod topology for various characteristics of the Chinese restaurant process.

Keywords: Chinese restaurant process; Random partitions; Random permutations; Point processes; Poisson measures; Vague convergence (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104793

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