Edwards–Wilkinson fluctuations in the Howitt–Warren flows

Jinjiong Yu

Stochastic Processes and their Applications, 2016, vol. 126, issue 3, 948-982

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.

Keywords: Edwards–Wilkinson fluctuations; Howitt–Warren flows; Sticky Brownian motions; Quenched invariance principle (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:3:p:948-982

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DOI: 10.1016/j.spa.2015.10.006

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