A hydrodynamic limit and fluctuations for a Chinese restaurant-like process

TL;DR

This paper investigates a spatial variant of the Chinese restaurant process derived from the Pólya sum process, analyzing its hydrodynamic limit and fluctuations, and establishing connections to multi-particle random walks.

Contribution

It introduces a spatial Chinese restaurant-like process with new properties such as summation and coupling, and studies its hydrodynamic behavior and fluctuations.

Findings

Defined a spatial Chinese restaurant process with summation and coupling.

Analyzed the hydrodynamic limit of the process.

Discussed fluctuations and connections to multi-particle random walks.

Abstract

We study a Markov process constructed from the P\'olya sum process, which yields a kind of spatial version of the Chinese restaurant process, where each 'table' is assigned a 'location'. This construction firstly allows a definition of summation of independent processes, and secondly a monotone coupling for different parameters. Moreover, the process is related to a multi-particle random walk on the positive integers and its hydrodynamic limit and fluctuations are discussed.