Mia Deijfen: Competing growth on lattices and graphs

Abstract: Competing first passage percolation describes the growth of two competing infections on an underlying graph structure. It was first studied on the \(Z^d\)-lattice. The main question is if the infection types can grow to occupy infinite parts of the lattice simultaneously, the conjecture being that the answer is yes if and only if the infections grow with the same intensity. Recently, the model has also been analyzed on more heterogeneous graph structures, where the degrees of the vertices can have an arbitrary distribution. In this case, it turns out that also the degree distribution plays a role in determining the outcome of the competition. I will give a survey of existing results, both on \(Z^d\) and on heterogeneous graphs, and describe open problems.