Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

@article{Levine2008StrongSA,
  title={Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile},
  author={Lionel Levine and Yuval Peres},
  journal={Potential Analysis},
  year={2008},
  volume={30},
  pages={1-27}
}
The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work (Levine and Peres, Indiana Univ Math J 57(1):431–450, 2008). For the shape consisting of $n=\omega_d r^d$ sites, where ωd is the volume of the unit ball in $\mathbb{R}^d$, we show that the inradius of the set of occupied sites is… 

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