Anomalous diffusion in comb-shaped domains and graphs
| Autor: | Gautam Iyer, James Nolen, Robert L. Pego, Samuel Cohn |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
Anomalous diffusion Oscillation Applied Mathematics General Mathematics Probability (math.PR) Mathematical analysis 60G22 (Primary) 35B27 (Secondary) Probabilistic logic 01 natural sciences 010101 applied mathematics Planar Mathematics::Probability Local time Convergence (routing) FOS: Mathematics Neumann boundary condition 0101 mathematics Mathematics - Probability Brownian motion |
| Zdroj: | Communications in Mathematical Sciences. 18:1815-1862 |
| ISSN: | 1945-0796 1539-6746 |
| DOI: | 10.4310/cms.2020.v18.n7.a2 |
| Popis: | 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). 47 pages, 4 figures |
| Databáze: | OpenAIRE |
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