[STAT/AP] Joost Jorritsma: Component sizes in spatial random graphs

08 April 2024 15:45 till 16:45 - Location: Lecture Hall D@ta | Add to my calendar

In a series of papers with Júlia Komjáthy and Dieter Mitsche, we uncovered the relation between three connected components in a large class of supercritical spatially embedded random graphs. This class includes amonst others long-range percolation and geometric inhomogeneous random graphs. We identify a single exponent zeta depending on the model parameters that describes the asymptotics of

1. the probability that the largest connected component is much smaller than expected;
2. the size of the second-largest component;
3. the distribution of the size of the component containing a distinguished vertex.

During the talk, I will explain the relation between the three quantities for long-range percolation. Time permitting, I discuss the probability that the largest component is much larger than expected: it behaves drastically different compared to (1) for models in which the degree distribution decays as a power law. This translates to a heavy upper tail of the final epidemic size when one considers epidemics on contact networks with superspreaders present.