A Central Limit Theorem for Modified Massive Arratia Flow

TL;DR

This paper proves a central limit theorem for the cluster positions in a modified massive Arratia flow, modeling particle aggregation in a fluid, using coupling with Brownian motions to analyze the system's statistical behavior.

Contribution

It introduces a central limit theorem for the modified massive Arratia flow, a new result in the study of particle cluster dynamics with mass aggregation effects.

Findings

Establishes a CLT for the point process of cluster positions.

Uses coupling with independent Brownian motions for critical mixing estimates.

Analyzes the system starting from a uniform initial configuration.

Abstract

The modified massive Arratia flow is a model for the dynamics of passive particle clusters moving in a random fluid that accounts for the effects of mass aggregation. We show a central limit theorem for the point process associated to the cluster positions when the system is started from a uniform configuration. The critical mixing estimate is obtained by coupling the system to countably many independent Brownian motions.