The winner takes it all
Competing first passage percolation describes the growth of two competing infections and was first studied on the Zd-lattice. We study competing first passage percolation on a more heterogeneous graph structure, where the degrees of the vertices follow a power-law distribution with finite mean but infinite variance. The main question is if the infection types can coexist, that is, if they can grow to occupy positive fractions of the vertex set simultaneously. I will elaborate on the answer, given in the title, and contrast this with the situation on Zd.