  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 Deffuant 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 differ by more
than a given threshold value $\theta$. We consider the two-sidedly infinite
path $\mathbb{Z}$ 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 finite-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.
