3:00 p.m., Friday (March 3, 2006)

MATX 1100

Martin Barlow

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).

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