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arXiv · 1612.03701

Perfect boundaries in rotor-router aggregation on cylinders

V. B. Priezzhev
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Abstract

We study a rotor-router version of the internal diffusion-limited aggregation introduced by J.Propp. The existing estimations of boundary fluctuations of the aggregation cluster show that they grow not faster than $O(\log r)$ with the cluster radius $r$. We consider the rotor-router internal DLA on the semi-infinite cylinder and prove a constant width of boundary fluctuations not depending on the radius of the cylinder.

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V. B. Priezzhev. 2016-12-12. Perfect boundaries in rotor-router aggregation on cylinders. https://doi.org/10.1088/1751-8121%2Faa7316

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