Journal of Combinatorics

Volume 3 (2012)

Number 2

Recurrent rotor-router configurations

Pages: 185 – 194



Omer Angel (Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada)

Alexander E. Holroyd (Microsoft Research, Redmond, Wash., U.S.A.)


We prove the existence of recurrent initial configurations for therotor walk on many graphs, including $Z^d$, and planar graphs withlocally finite embeddings. We also prove that recurrence andtransience of rotor walks are invariant under changes in the startingvertex and finite changes in the initial configuration.


rotor walk, rotor-router, quasi-random, recurrence

2010 Mathematics Subject Classification

05C25, 82C20

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