Further results on the consensus formation in the Deffuant model

The so-called Deffuant model describes a pattern for social interaction, in which two neighboring individuals randomly meet and share their opin-ions on a certain topic, if their discrepancy is not beyond a given threshold θ. The major focus of the analyses, both theoretical and based on simula-tions, lies on whether these single interactions lead to a global consensus in the long run or not. First, we generalize a result of Lanchier for the Deffuant model on Z, determining the critical value for θ at which a phase transition of the long term behavior takes place, to other distributions of the initial opinions than i.i.d. uniform on [0, 1]. Then we shed light on the situations where the underlying line graph Z is replaced by higher-dimensional lattices Zd, d ≥ 2, or the infinite cluster of supercritical i.i.d. bond percolation on these lattices.