Edwards-Wilkinson fluctuations in the Howitt-Warren flows

TL;DR

This paper investigates current fluctuations in a dual smoothing process related to Howitt-Warren flows, revealing they follow the Edwards-Wilkinson universality class with Gaussian limits and establishing a quenched invariance principle.

Contribution

It demonstrates that current fluctuations in the dual smoothing process belong to the Edwards-Wilkinson universality class and proves a quenched invariance principle for the associated random motion.

Findings

Current fluctuations scale as t^{1/4} and converge to a Gaussian process.

Centered quenched mean process also converges to a Gaussian process.

Established a quenched invariance principle for the random motion in Howitt-Warren flow.

Abstract

We study current fluctuations in a one-dimensional interacting particle system known as the dual smoothing process that is dual to random motions in a Howitt-Warren flow. The Howitt-Warren flow can be regarded as the transition kernels of a random motion in a continuous space-time random environment. It turns out that the current fluctuations of the dual smoothing process fall in the Edwards-Wilkinson universality class, where the fluctuations occur on the scale $t^{1/4}$ and the limit is a universal Gaussian process. Along the way, we prove a quenched invariance principle for a random motion in the Howitt-Warren flow. Meanwhile, the centered quenched mean process of the random motion also converges on the scale $t^{1/4}$, where the limit is another universal Gaussian process.