  We consider a stochastic, continuous state and time opinion model where each
agent's opinion locally interacts with other agents' opinions in the system,
and there is also exogenous randomness. The interaction tends to create
clusters of common opinion. By using linear stability analysis of the
associated nonlinear Fokker-Planck equation that governs the empirical density
of opinions in the limit of infinitely many agents, we can estimate the number
of clusters, the time to cluster formation and the critical strength of
randomness so as to have cluster formation. We also discuss the cluster
dynamics after their formation, the width and the effective diffusivity of the
clusters. Finally, the long term behavior of clusters is explored numerically.
Extensive numerical simulations confirm our analytical findings.
