Math Graduate Student Seminar

Let G be a transitive connected graph. Bernoulli bond percolation on G is the random graph obtained from G by independently setting each edge open (retained) or closed (deleted), with probability p of being open. A central problem of percolation theory is to understand the number of infinite clusters and how this number depends on the parameter p and the structure of the graph. I will present both classical results and recent progress on this topic, as well as my joint work with Hutchcroft.