Rotor-Router Aggregation on the Comb

Details Rotor-Router Aggregation on the Comb Rotor-Router Aggregation on the Comb

2011-03-24

arxiv.org/abs/1103.4797v4

The Electronic Journal of Combinatorics 18(2011), P 224

Mathematics

Combinatorics

23 pages, 4 figures

Scientific paper

We prove a shape theorem for rotor-router aggregation on the comb, for a specific initial rotor configuration and clockwise rotor sequence for all vertices. Furthermore, as an application of rotor-router walks, we describe the harmonic measure of the rotor-router aggregate and related shapes, which is useful in the study of other growth models on the comb. We also identify the shape for which the harmonic measure is uniform. This gives the first known example where the rotor-router cluster has non-uniform harmonic measure, and grows with different speeds in different directions.

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