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

Averaging plus Learning Models and Their Asymptotics