Lukas Lüchtrath (Wias Berlin) – The contact process on one-dimensional scale-free networks

Notes: unusual time.

We study the survival/extinction phase transition for contact processes with quenched disorder. The disorder is given by a locally finite random graph with vertices indexed by Z that is assumed to be invariant under index shifts and augments the nearest-neighbour lattice by additional longrange edges. We provide sufficient conditions that imply the existence of a subcritical phase and therefore the non-triviality of the phase transition. Our results particularly apply to instances of scale-free random geometric graphs with any integrable degree distribution. This contrasts the behaviour of the process on Galton-Watson trees for which the existence of an extinction phase is equivalent to light-tailedness of the offspring (i.e. degree) distribution. We further discuss potential extensions to higher dimension. The talk is based on joint work with Benedikt Jahnel and Christian M¨onch.