Random walks on dynamic random graphs

Frank den Hollander (Leiden)
Wednesday, April 19, 2017 - 6:15pm
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

The mixing time of a Markov chain is the time it needs to approach its stationary distribution. For random walks on graphs, the characterisation of the mixing time has been the subject of intensive study. One of the motivations is the fact that the mixing time gives information about the geometry of the graph. In the last few years, much attention has been devoted to the analysis of mixing times for random walks on random graphs, which poses interesting challenges.
Many real-world networks are dynamic in nature. It is therefore natural to study random walks on dynamic random graphs. In this talk we consider a random walk on the configuration model, i.e., a random graph with prescribed degrees. We investigate what happens when at each unit of time a fraction \alpha_n of the edges is randomly relocated, where n is the number of nodes. We identify three regimes for the mixing time in the limit as n \to \infty, depending on the choice of \alpha_n. These regimes exhibit surprising behaviour.
Joint work with Luca Avena (Leiden), Hakan Guldas (Leiden) and Remco van der Hofstad (Eindhoven)