*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.