02.07.2018 17:30 Harald Koppen (LMU, MSc presentation):
Sharpness of the Phase Transition in the Contact ProcessB 252 (Theresienstr. 39, 80333 München)

The contact process is an interacting particle system which can be interpreted as the spread of an infection. In this talk, we focus on the contact process on the two-dimensional integer lattice and consider the percolation transition. That is, we examine the size of the occupied cluster of the origin subject to the upper invariant measure. It is well known that there is a critical value \lambda_c such that for all infection rates bigger than \lambda_c, the upper invariant measure is non-trivial. Furthermore, there is another critical value \lambda_p such that the probability of the aforementioned cluster being infinite is bigger than zero for all infection rates bigger than \lambda_p. However, if the infection rate is smaller than \lambda_p, the distribution of the size of the cluster has an exponential tail. We sketch a proof of this result using techniques as in the proof of a related result for confetti percolation. A short introduction to the contact process will be given at the beginning of the talk.