Friday October 7th at 3.30pm

neighbors in each direction and then rewiring a small fraction p of connections. One can in a straightforward way define a two dimensional

version starting from a torus. This gives a graph that is a more reasonable model for the spread of infectious diseases. We get colds and

the flu not only from our next door neighbors in suburbia, but also from people we see at work and from germs our children bring home from school.

Motivated by this story, we will investigate the behavior of epidemics, percolation, the Ising model, random walks, and the voter model on the

small world graph and compare their behavior to processes on regular lattices. The talk will cover parts of Chapters 5 and 6 of my almost

finished book which can be found at http://www.math.cornell.edu/~durrett/