  A rotor-router walk on a graph is a deterministic process, in which each
vertex is endowed with a rotor that points to one of the neighbors. A particle
located at some vertex first rotates the rotor in a prescribed order, and then
it is routed to the neighbor the rotor is now pointing at. In the current work
we make a step toward in understanding the behavior of rotor-router walks on
random trees. More precisely, we consider random i.i.d. initial configurations
of rotors on Galton-Watson trees, i.e. on a family tree arising from a
Galton-Watson process, and give a classification in recurrence and transience
for rotor-router walks on these trees.
