The central limit theorem for the number of clusters of the Arratia flow

TL;DR

This paper proves a central limit theorem for the number of clusters in the Arratia flow as the initial interval grows, and provides an estimate of the convergence rate.

Contribution

It establishes the CLT for cluster counts in the Arratia flow and quantifies the convergence rate with a Berry-Esseen type estimate.

Findings

Proved the CLT for the number of clusters in the Arratia flow.

Derived a Berry-Esseen type estimate for the convergence rate.

Quantified the asymptotic distribution of cluster counts.

Abstract

In this paper we prove the central limit theorem for the number of clusters formed by the particles of the Arratia flow starting from the interval $[0;n]$ as $n\to\infty$ and obtain an estimate of the Berry-Esseen type for the rate of this convergence.