Rotor walks on general trees

Understand

The rotor walk on a graph is a deterministic analogue of random walk.

• Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits.
• We consider rotor walk on an infinite rooted tree, restarted from the root after each escape to infinity.
• We prove that the limiting proportion of escapes to infinity equals the escape probability for random walk, provided only finitely many rotors send the walker initially towards the root.