2014/12/12 by Jinjiong Yu, Yu, Jinjiong · 2 citations
Mathematics · Physics and Astronomy · #60F17 #60K35 #60K37 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60F17 #msc:60K35 #msc:60K37
paper · pdf · doi:10.48550/arxiv.1412.3911
32 pages, typos corrected, to appear in Stochastic Processes and their Applications. arXiv admin note: text overlap with arXiv:1011.3895 by other authors
openalex publication_date 2014/12/12 · arxiv created 2015/11/08 · arxiv updated 2015/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.