The Rotor-Router Model on Regular Trees

Understand

The rotor-router model is a deterministic analogue of random walk.

• It can be used to define a deterministic growth model analogous to internal DLA.
• We show that the set of occupied sites for this model on an infinite regular tree is a perfect ball whenever it can be, provided the initial rotor configuration is acyclic (that is, no two neighboring vertices have rotors pointing to one another).
• This is proved by defining the rotor-router group of a graph, which we show is isomorphic to the sandpile group.