Speaker: Robert M. Ziff (U-M Engineering)
In the past few years, there has been a great deal of interest in a variant on percolation growth called "explosive percolation." In this model, two alternative bonds are considered for adding to the system, and the one that connects the smaller pairs of clusters (by some measure, such as the product rule) is chosen. The resulting transition is very sharp. While originally thought to be discontinuous (like in a first-order phase transition), it is now seen to be continuous for some models at least. In any case, the transition is very sharp, and the model has been applied to problems such as the human protein homology network and nanotube clustering, and has been studied on Erdos-Renyi random graphs, scale-free networks, and regular lattices.