  The paper treats an agent-based model with averaging dynamics to which we
refer as the K-averaging model. Broadly speaking, our model can be added to the
growing list of dynamics exhibiting self-organization such as the well-known
Vicsek-type models [1, 2, 29]. In the $K$-averaging model, each of the $N$
particles updates their position by averaging over $K$ randomly selected
particles with additional noise. To make the $K$-averaging dynamics more
tractable, we first establish a propagation of chaos type result in the limit
of infinite particle number (i.e. $N \to \infty$) using a martingale technique.
Then, we prove the convergence of the limit equation toward a suitable Gaussian
distribution in the sense of Wasserstein distance as well as relative entropy.
We provide additional numerical simulations to illustrate both results.
