  We develop original models to study interacting agents in financial markets
and in social networks. Within these models randomness is vital as a form of
shock or news that decays with time. Agents learn from their observations and
learning ability to interpret news or private information in time-varying
networks. Under general assumption on the noise, a limit theorem is developed
for the generalised DeGroot framework for certain type of conditions governing
the learning. In this context, the agents beliefs (properly scaled) converge in
distribution that is not necessarily normal. Fresh insights are gained not only
from proposing a new setting for social learning models but also from using
different techniques to study discrete time random linear dynamical systems.
