Edwards-Wilkinson fluctuations in the Howitt-Warren flows

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• 作者：Jinjiong Yu ^{yujinjiong@nus.edu.sg" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60K35 ; 60K37 ; 60F17
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：126
• 期：3
• 页码：948-982
• 全文大小：376 K

文摘

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$t^{1/4}$ 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$t^{1/4}$, where the limit is another universal Gaussian process.