Colloquium Mathematics - Prof. dr. D. Valesin University of Groningen

Title: Percolation on stationary distributions of interacting particle systems

Abstract:

In site percolation, vertices of a graph are declared to be
open or closed according to some random procedure. One then studies
the subgraph induced by the open vertices; percolation is said to
occur if this subgraph has infinite connected components. Many
percolation models exhibit a phase transition with respect to the
density of open vertices: percolation occurs if and only if this
density is above a certain critical threshold. In models where the
open/closed state is chosen with dependence among different vertices,
proving a percolation phase transition occurs can be challenging. In
this talk we will address models in which the states are sampled from
probability distributions obtained from the equilibrium states of
interacting particle systems. We will discuss two important classes of
interacting particle systems, namely the voter model and the contact
process. In both cases, we prove that (under certain assumptions on
the system dynamics) a percolation phase transition is present. Joint
work with Balázs Ráth (BME, Hungary).