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Scaling limit for small blocks in the Chinese restaurant process

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  • Galganov, Oleksii
  • Ilienko, Andrii

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.

Suggested Citation

  • Galganov, Oleksii & Ilienko, Andrii, 2026. "Scaling limit for small blocks in the Chinese restaurant process," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:spapps:v:192:y:2026:i:c:s0304414925002376
    DOI: 10.1016/j.spa.2025.104793
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    References listed on IDEAS

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    1. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    2. Stark, Dudley, 2024. "Markov chains generating random permutations and set partitions," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
    3. Galganov, Oleksii & Ilienko, Andrii, 2024. "Short cycles of random permutations with cycle weights: Point processes approach," Statistics & Probability Letters, Elsevier, vol. 213(C).
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