Cornell Math - MATH 777, Fall 2004

MATH 777: Random Graphs (Fall 2004)

Instructor: Richard Durrett

Meeting Time & Room

www.math.cornell.edu/~durrett/math777/math777.html

The study of random graphs began in the 1950s with classic papers of Erdos and Renyi. In the last half-dozen years, the Watts and Strogatz small world model and Barbasi's preferential attachment model have led to an explosion of new work much of it non-rigorous, see my book review in the February 2004 Notices. I'll start the course with the classic Erdos-Renyi model but then move on to the Molloy and Reed model with general degree distribution, Storgatz-Watts small world, Barbasi's preferential attachment model, the Calloway-Hopcroft-Kleinberg-Newman-Strogatz randomly grown graph with its Kosterlitz Thouless transition (recently proved by Bollobas, Riordan and Janson), and then look at processes like epidemics, random walks, and the voter model taking place on random graphs. There is no book for the class. Instead we will read a series of articles.