Cut points for simple random walks

Speaker: 
Daisuke Shiraishi
Date: 
Tue, Jun 5, 2012
Location: 
PIMS, University of British Columbia
Conference: 
PIMS-MPrime Summer School in Probability
Abstract: 
We consider two random walks conditioned “never to intersect” in Z^2. We show that each of them has infinitely many `global' cut times with probability one. In fact, we prove that the number of global cut times up to n grows like n^{3/8}. Next we consider the union of their trajectories to be a random subgraph of Z^2 and show the subdiffusivity of the simple random walk on this graph.