Consensus formation in the Deffuant model
Deffuant and Weisbuch introduced a model of interacting agents which is quite
popular among social scientists to shape and study the formation of collective
opinions. Given an underlying graph of connections between the individuals,
neighbours randomly meet and start compromising if their opinions are not too
far apart.
The crucial question of the system's long term behavior has been answered to
an almost complete extent for the line graph and initial opinions which are i.i.d.
uniform on [0,1] by Lanchier in 2011.
In this talk, I will give a short introdution to the topic, a summary of the
ideas used to prove the just mentioned result and then present the results
dealing with extensions to other starting distributions, higher-dimensional grids
and the infinite cluster of supercritical bond percolation on the latter.
(Joint work with O. Häggström)