# Averaging plus Learning Models and Their Asymptotics

## TL;DR

This paper introduces new models for social learning in financial and social networks, analyzing how agents' beliefs evolve over time with randomness and learning, revealing non-normal convergence behaviors.

## Contribution

It develops a novel framework for studying agents' learning dynamics with stochastic shocks and provides a limit theorem for belief convergence in these models.

## Key findings

- Beliefs converge in distribution, not necessarily normally.
- New insights into stochastic social learning models.
- Application of advanced techniques to random linear systems.

## Abstract

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.