Spherical Asymptotics for the Rotor-Router Model in Z^d

Preprint

14 March 2005

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0503251

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

AGGREGATION MODEL
ROTOR ROUTER
ROUTER MODEL
RANDOM WALK
MODEL IN Z
INVENTED
WALK

All Related Versions

Version 1, 2005-03-14, ArXiv
Published version: Indiana University Mathematics Journal, 57 (1), 431.

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