Math 288 Topics in Probability Theory
Title: Random Graphs
Instructor: Rick Durrett

The course will be an introduction to random graphs which will begin by
following my book Random Graph Dynamics. We'll begin with the classic story
of the Erdos-Renyi random graph and the phase transition which results in a
giant component. We will then consider other degree distributions
(especially those with a power law tail) and other algorithms for generating
graphs: the small world model, preferential attachment, and the CHKNS
procedure which grows a random graph with a very interesting
(Kosterlitz-Thouless) phase transition.

Once we have mastered the geometry of random graphs we will turn to the
study of dynamics taking place on them: epidemics, random walks, the voter
model, etc. Much of this material is more recent than my book, see e.g., my
article "Some features of the spread of epidemics and information on a
random graph." PNAS 107 (2010), 4491-4498.

Our emphasis will be on proving theorems, but we will emphasize ideas behind
the proofs rather than slugging through all the details so it should
tolerable for those who want to know what is true rather than why. This
course should be a good introduction to the activities at the SAMSI year on
complex networks which will have its own tutorial course.