  Understanding the evolution of collective beliefs is of critical importance
to get insights on the political trends as well as on social tastes and
opinions. In particular, it is pivotal to develop analytical models that can
predict the beliefs dynamics and capture the interdependence of opinions on
different subjects. In this paper we tackle this issue also accounting for the
individual endogenous process of opinion evolution, as well as repulsive
interactions between individuals' opinions that may arise in the presence of an
adversarial attitude of the individuals. Using a mean field approach, we
characterize the time evolution of opinions of a large population of
individuals through a multidimensional Fokker-Planck equation, and we identify
the conditions under which stability holds. Finally, we derive the steady-state
opinion distribution as a function of the individuals' personality and of the
existing social interactions. Our numerical results show interesting dynamics
in the collective beliefs of different social communities, and they highlight
the effect of correlated subjects as well as of individuals with an adversarial
attitude.
