On recurrence and transience of self-interacting random walks

Let µ₁,...,µ _k be d-dimensional probabilitymeasures in ? ^d with mean 0. At each time we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. In particular, in dimension 3 we give the complete picture: every walk generated by two measures is transient and there exists a recurrent walk generated by three measures.