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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

Subject: Mathematics, Probability

Class: Scientific

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.