Spherical Asymptotics for the Rotor-Router Model in Z^d
Probability
2010-10-11 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.math/0503251,
title = {Spherical Asymptotics for the Rotor-Router Model in Z^d},
author = {Lionel Levine and Yuval Peres},
journal= {arXiv preprint arXiv:math/0503251},
year = {2010}
}
Comments
19 pages, 2 figures