Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/135178
Title: ON THE BROWNIAN NET AND THE HOWITT-WARREN FLOWS
Authors: YU JINJIONG
Keywords: Branching-coalescing nonsimple random walks, weak convergence, the Brownian net, the Howitt-Warren flows, the Edwards-Wilkinson universality class
Issue Date: 19-Aug-2016
Citation: YU JINJIONG (2016-08-19). ON THE BROWNIAN NET AND THE HOWITT-WARREN FLOWS. ScholarBank@NUS Repository.
Abstract: The Brownian net is a collection of branching-coalescing Brownian motions starting from every point in the space-time plane R^2, which has been shown to be the diffusive scaling limit of branching-coalescing simple random walks, where the random walk paths do not cross. The first part of the thesis is devoted to showing that the Brownian net is contained in any subsequential weak limit of nonsimple random walks with crossing paths. In the second part, 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 family of transition kernels of a random motion in a continuous space-time random environment, which can be constructed from the Brownian web and net. It turns out that the current fluctuations 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.
URI: http://scholarbank.nus.edu.sg/handle/10635/135178
Appears in Collections:Ph.D Theses (Open)

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