Overly determined agents prevent consensus in a generalized Deffuant model on ℤ with dispersed opinions

During the last decades, quite a number of interacting particle systems have been introduced and studied in the border area of mathematics and statistical physics. Some of these can be seen as simplistic models for opinion formation processes in groups of interacting people. In the one introduced by Deuant et al. agents, that are neighbors on a given network graph, randomly meet in pairs and approach a compromise if their current opinions do not dier by more than a given threshold value . We consider the two-sidedly innite path Z as underlying graph and extend former investigations to a setting in which opinions are given by probability distributions. Similar to what has been shown for nite-dimensional opinions, we observe a dichotomy in the long-term behavior of the model, but only if the initial narrow-mindedness of the agents is restricted.