Propagation of chaos and the many-demes limit for weakly interacting diffusions in the sparse regime

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 exchange- able 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.


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