UCSD MATHEMATICS DEPARTMENT: PROBABILITY SEMINAR
Vlada Limic, Cornell University
Once reinforced walk on a regular tree
Consider a nearest neighbor walk on a regular tree, with
transition probabilities proportional to weights or conductances
of the edges. Initially all edges have weight 1, and the weight
of an edge is increased to c > 1 when the edge is traversed
for the first time. After such a change the weight of an edge
stays at $c$ forever. We show that this walk is transient for
all values of c > 1, and moreover that it has a positive speed.
We also prove an invariance principle for the height of the walk.
This is a joint work with Rick Durrett and Harry Kesten.