Spherical asymptotics for the rotor-router model in $\mathbb{Z}^d$
- 1 January 2008
- journal article
- Published by Indiana University Mathematics Journal in Indiana University Mathematics Journal
- Vol. 57 (1) , 431-450
- https://doi.org/10.1512/iumj.2008.57.3022
Abstract
The rotor-router model is a deterministic analogue of random walk invented by Jim Propp. It can be used to define a deterministic aggregation model analogous to internal diffusion limited aggregation. We prove an isoperimetric inequality for the exit time of simple random walk from a finite region in Z^d, and use this to prove that the shape of the rotor-router aggregation model in Z^d, suitably rescaled, converges to a Euclidean ball in R^d.Comment: 19 pages, 2 figureKeywords
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