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The aim of this note is to extend the result of Angel and Holroyd concerningthe transience and the recurrence of transfinite rotor-router walks, for randominitial configuration of rotors on homogeneous trees. We address the samequestion on directed covers of finite graphs, which are also called trees withfinitely many cone types or periodic trees. Furthermore, we provide an exampleof a directed cover such that the rotor-router walk can be either recurrent ortransient, depending only on the planar embedding of the periodic tree.

Transience and recurrence of rotor-router walks on directed covers of graphs