Generalised graphical representations
Abstract.
Numerous dynamic spatial models feature interactions between particles that are based on waiting times; the most prominent examples being first passage percolation, where a fluid spreads from a source, and the contact process, where an infection spreads on a graph with the possibility of recovery. However, waiting times are unnatural for certain models. One can argue that people have a daily routine and meet each other on a relatively fixed schedule, rather than a random waiting time after having met someone else. With the help of graphical representations, we develop a framework that moves away from waiting times towards so called contact times. As an application, we present results on a first contact percolation model, where people follow a random daily meeting routine, as well as contact processes with periodic recoveries.