Spherical asymptotics for the rotor-router model in $\mathbb{Z}^d$

Abstract

The rotor-router model is a deterministic analogue of random walk invented by\nJim Propp. It can be used to define a deterministic aggregation model analogous\nto internal diffusion limited aggregation. We prove an isoperimetric inequality\nfor the exit time of simple random walk from a finite region in Z^d, and use\nthis to prove that the shape of the rotor-router aggregation model in Z^d,\nsuitably rescaled, converges to a Euclidean ball in R^d.\n