[STAT/AP] Bert Zwart: Large deviations for heavy tails and triangles in scale-free random graphs

18 December 2023 15:45 till 16:45 - Location: Timmanzaal LB.01.170 | Add to my calendar

in the first half of this talk, we give an overview of how heavy-tailed phenomena can originate and propagate in stochastic systems. In particular, we review recent results on sample-path large deviations, a connection with impulse control problems, and several illustrative examples.

After that, we focus in more detail on a particular problem related to triangle counts in random graphs: we provide large deviation estimates for the upper tail of the number of triangles in scale-free inhomogeneous random graphs where the degrees have power law tails. We show that the upper tail exhibits a phase transition, where the rare event of interest is caused by a single, or by many big hubs. Our proofs are partly based on various concentration inequalities. In particular, we tailor concentration bounds for empirical processes, going back to Wellner (1978),
to make them well-suited for analyzing heavy-tailed phenomena in nonlinear settings.

Joint work with Clara Stegehuis (University of Twente)