3:00 p.m., Friday (March 3, 2006)
Random walks, the heat equation, and percolation
I will discuss `homogenization' of the heat equation in a random environment.
The environment is given by bond percolation on the Euclidean lattice Z^d:
each bond is present (or open) with probability p, and closed (absent) with
probability 1-p, independently of all other bonds. When p is large enough,
this graph has a single infinite connected component, but this has arbitrarily
large holes and bottlenecks. Nevertheless we can now say a great deal about the
heat equation (or the random walk) on this set. The talk will end with some simulations.
Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).