Yuval Peres: Transience, recurrence and collisions  for controlled random walks

Speaker: Yuval Peres

Title: Transience, recurrence and collisions  for controlled random walks

Abstract: Fix k probability measures on R^d with mean 0 and bounded, d-dimensional support. At each positive integer time we choose one of the k measures based on the history of the process and take a step according to that measure. Transience and recurrence of such walks depends in a delicate way on the measures used; we understand the picture in dimension 3 and higher but dimension 2 leaves some open problems.   This part is joint work with Serguei Popov and Perla Sousi.  In the second part of the talk, I will discuss the collision property of a graph G, i.e., when do two simple random walks on G have infinitely many collisions a.s.?