Year: 2011
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Huss, Wilfried, Sava, Ecaterina
Institutions: University of Siegen, Graz University of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951420339