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

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

2005-03-14

arxiv.org/abs/math/0503251v1

Indiana Univ. Math. J. 57: 431--450, 2008

Mathematics

Probability

19 pages, 2 figures

Scientific paper

10.1512/iumj.2008.57.3022

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.

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