Discrete Mathematics and Optimization Seminar

Rick Durrett
Cornell University
Friday October 7th at 3.30pm
McConnell Room 13 (SOCS Colloquium)

Title. Life in a Small World.

Abstract. In 1998 Strogatz and Watts created their small world random graph by starting with a ring of sites each of which was connected to its k nearest
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/