LCN2 seminar November 2023
- Friday 24 November 2023
- Room 312
62nd LCN2 seminar
Speaker: Federico Capannoli (Leiden University, MI)
Title: Voter model on sparse random digraphs
We consider Markovian dynamics on a typical realization of the so-called Di- rected Configuration Model (DCM), which is a random directed graph with prescribed
in- and out-degrees. In this random geometry, we study the consensus time of the voter model on a typical realization of the graph and the meeting time of two random walks starting at stationarity. Indeed, it is known that the latter two quantities are related to each other when the underlying sequence of graphs satisfies certain mean field conditions. We provide a complete characterization of the distribution of meeting and consensus time on a typical random graph as a function of a single quantity θ. More precisely we show that, for a typical large graph from the DCM ensemble, the distribution of the meeting time is well-approximated by an exponential random variable. Furthermore, we provide the precise first-order approximation of its expectation, showing that the latter is linear in the size of the graph, and the explicit preconstant θ depends on some easy statistics of the degree sequence. As a consequence, we can analyze the effect of the degree sequence on the expected meeting time and, via some explicit examples, how its regularity/variability play crucial roles in the information diffusion.
This is based on a joint work with Luca Avena (University of Florence), Rajat Subhra Hazra (Leiden University) and Matteo Quattropani (Sapienza, University of Rome).
Afterwards there will be drinks in the Foobar.