Lecture
LCN2 Seminar: Discordant edges for the voter model on regular random graphs.
- Date
- Friday 28 October 2022
- Time
- Location
- Snellius room 313
We consider the continuous-time model for the evolution of two opinions in a population, known as the voter model, on random networks. In this setting, nodes represent individuals in the population while interaction between individuals are represented by links. At random indendependent times, links are activated and when that happens, one of the two individuals connected by such link receives the opinion of its neighbor. In a finite connected network, the system eventually fixates in a consensus configuration, where all nodes share the same opinion. Our interest lies in understanding how this consensus is achieved. In particular, we examine the time-evolution of the density of the discordant edges (i.e. edges with different opinions at their endvertices) until consensus is reached when the network is given by a random graph with constant degree d. In this case, the density of discordant edges undergoes a quasi-stationary-like evolution which we make precise. Joint work with Luca Avena, Rajat Hazra, Frank den Hollander and Matteo Quattropani.