Event Type:

Department Colloquium

Date/Time:

Tuesday, May 30, 2006 - 08:00

Location:

Kidd 364

Guest Speaker:

Institution:

U. Washington

Abstract:

The ergodic theorem is a powerful tool in probability. Its use involves considering a probabilistic model as a dynamical system. The ergodic theorem has been particularly useful in studying percolation, where it has been used to construct simple geometric proofs to a number of difficult problems. In this talk I will discuss three such applications: 1) Burton and Keane's proof that there is a unique infinite supercritical percolation cluster, 2) Berger and Biskup's proof that simple random walk on the infinite percolation cluster converges to Brownian motion, and 3) A proof that coexistence is possible in Richardson's growth model.