Rotor-Router Aggregation on the Layered Square Lattice
Name
Kager-2010-Roter-router aggregation.pdf
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237.63 KB
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Checksum (MD5)
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Author(s)
Kager, Wouter
Levine, Lionel
Date Issued
November 2010
Journal
Electronic Journal of Combinatorics
Publisher
Electronic Journal of Combinatorics
Citation
Kager, Wouter, and Lionel Levine. "Rotor-Router Aggregation on the Layered Square Lattice." Electronic Journal of Combinatorics, Volume 17 (2010).
Version
Final published version
Abstract
In rotor-router aggregation on the square lattice Z[superscript 2], particles starting at the origin perform deterministic analogues of random walks until reaching an unoccupied site. The limiting shape of the cluster of occupied sites is a disk. We consider a small change to the routing mechanism for sites on the x- and y-axes, resulting in a limiting shape which is a diamond instead of a disk. We show that for a certain choice of initial rotors, the occupied cluster grows as a perfect diamond.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.37236/424
