  Propagation of chaos is a well-studied phenomenon and shows that weakly
interacting diffusions may become independent as the system size converges to
infinity. Most of the literature focuses on the case of exchangeable systems
where all involved diffusions have the same distribution and are "of the same
size". In this paper, we analyze the case where only a few diffusions start
outside of an accessible trap. Our main result shows that in this "sparse
regime" the system of weakly interacting diffusions converges in distribution
to a forest of excursions from the trap. In particular, initial independence
propagates in the limit and results in a forest of independent trees.
