# A note on weak convergence of the $n$-point motions of Harris flows

## TL;DR

This paper extends previous results on the weak convergence of Harris flows' n-point motions to the Arratia flow, specifically when the covariance functions converge to a measure-zero support, broadening the understanding of these stochastic processes.

## Contribution

It generalizes the weak convergence results of Harris flows to cases with covariance functions supported on measure-zero sets, expanding the applicability of previous theorems.

## Key findings

- Weak convergence established for Harris flows with covariance functions supported on measure-zero sets.
- Extension of convergence results to more general covariance functions.
- Provides theoretical foundation for analyzing Harris flows with singular covariance structures.

## Abstract

In this note we extend the main results of [2] and [8], which concern the weak convergence of the $n$-point motions of smooth Harris flows to those of the Arratia flow, to the case when the covariance functions of these Harris flows converge pointwise to a covariance function whose support is of zero Lebesgue measure.