Anomalous diffusion in comb-shaped domains and graphs
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Publication:2023510
DOI10.4310/CMS.2020.V18.N7.A2zbMATH Open1459.60215arXiv1809.01601OpenAlexW3111968055MaRDI QIDQ2023510
Author name not available (Why is that?)
Publication date: 3 May 2021
Published in: (Search for Journal in Brave)
Abstract: In this paper we study the asymptotic behavior of Brownian motion in both comb-shaped planar domains, and comb-shaped graphs. We show convergence to a limiting process when both the spacing between the teeth emph{and} the width of the teeth vanish at the same rate. The limiting process exhibits an anomalous diffusive behavior and can be described as a Brownian motion time-changed by the local time of an independent sticky Brownian motion. In the two dimensional setting the main technical step is an oscillation estimate for a Neumann problem, which we prove here using a probabilistic argument. In the one dimensional setting we provide both a direct SDE proof, and a proof using the trapped Brownian motion framework in Ben Arous etal (Ann. Probab. '15).
Full work available at URL: https://arxiv.org/abs/1809.01601
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