Pool model: a mass preserving multi particle aggregation process

TL;DR

This paper introduces the Pool model, a mass-preserving, rotationally symmetric analogue of MDLA, where particles perform random walks and are absorbed into a growing pool, with a novel Poisson process characterization.

Contribution

The paper develops the Pool model with mass-preserving dynamics and provides a new version of Kurtz's theorem for analyzing the conditioned particle field.

Findings

The pool's area growth is characterized by the model's dynamics.

A new Poisson process framework describes the particle field conditioned on pool growth.

The model offers insights into mass-preserving aggregation processes.

Abstract

We present and study the Pool model in $\mathbb{R}^2$, a rotationally symmetric analogue of Multi-Particle Diffusion-Limited Aggregation (MDLA), in which particles ("droplets") perform continuous-time random walks and are absorbed upon entering a circular pool initially centered at the origin. Each absorbed particle increases the pool's mass, and the pool expands so that its area grows accordingly, yielding a natural mass-preserving dynamics. A central tool which is of independent interest is a version of Kurtz's theorem for this model, depicting the field of particles conditioned on the growth of the pool as an independent non-homogeneous Poisson point process.