UTFacultiesEEMCSDisciplines & departmentsMORResearch Talk: Consensus time for voter model on random graphs: recent advances and some open problems

Research Talk: Consensus time for voter model on random graphs: recent advances and some open problems Luca Avena (University of Florence)

Abstract

We discuss the current state of the art in understanding consensus formation for the classical voter model on various random graph models. The voter model is a simple stochastic process in which each node in a network adopts the state of a randomly chosen neighbor at each time step, modeling opinion dynamics or information spreading. Since the ’90 it is well-understood that the time the voter model takes to achieve consensus on a given graph can be related to how a system of random walks fully coalesces. Despite this,  it is still unclear in various settings how the consensus time behaves as a function of the underlying network structure and in particular of its degree distribution, except for a few stylised models. In a series of recent rigorous and non-rigorous works, we have been investigating this question in great details for various classes of random graphs clarifying possible speed up or slow-down for the consensus formation in presence of directed or undirected links, some edge-dynamics, and heavy tailed degree distributions.

Based on recent works with: Baldasso, Capannoli, Garlaschelli, Hazra, den Hollander, Quattropani.