Wolfgang Woess (Graz)

Lamplighter random walks on trees

Let X be any graph (infinite, locally finite, connected). Suppose that at each vertex there is a lamp which may be in two states "off" or "on". Initially, all lamps are "off". A lamplighter performs a random walk in the graph. At each step he chooses at random whether to step to a neighbour vertex, or to change the state of the lamp where he stands (in more general models, he may combine actions of this type). A state of this Markov process consists of the actual position (vertex) of the lamplighter in X together with the configuration of lamps that are "on". The talk will describe several features of this class of random walks in the case when X is a tree, and in particular, when it is the two-way-infinite path: geometry of the state space, asymptotics of transtion probabilities, limit behaviour in space, rate of escape, harmonic functions.