Work

Scaling limit for small blocks in the Chinese restaurant process

Year: 2025

Type: article

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.

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2025.104793

Authors: Oleksii Galganov, Andrii Ilienko

Institutions: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, University of Bern

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,520

Funder: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung