ANOMALOUS DIFFUSION IN COMB-SHAPED DOMAINS AND GRAPHS

Journal Article

© 2020. All rights reserved. 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 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 et al. (Ann. Probab. ’15).

Full Text

Duke Authors

Cited Authors

  • COHN, S; IYER, G; NOLEN, J; PEGO, RL

Published Date

  • January 1, 2020

Published In

Volume / Issue

  • 18 / 7

Start / End Page

  • 1815 - 1862

Electronic International Standard Serial Number (EISSN)

  • 1945-0796

International Standard Serial Number (ISSN)

  • 1539-6746

Digital Object Identifier (DOI)

  • 10.4310/CMS.2020.V18.N7.A2

Citation Source

  • Scopus