Edwards–Wilkinson fluctuations in the Howitt–Warren flows

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 t1/4 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 t1/4, where the limit is another universal Gaussian process.