Seminar to be held in Room 107, 24 Hillhouse Ave at 4:15 pm
Paul Erdos and Alfred Renyi showed thirty years ago that the random graph G(n,p) undergoes percolation (what they called The Double Jump) at p=1/n. Today we know how to slow down the process, using the parametrization np-1=an^{-1/3}. We approach this through classic percolation, considering a branching process with mean near one. The infinite and finite components have analogs in our finite, asymptotic, case. As a surprising Corollary we get asymptotic enumeration of unicylic (bicyclic, etc.) graphs in terms of moments of the area under a Brownian Bridge.