On the scaling limit of finite vertex transitive graphs with large diameter

Itai Benjamini, Hilary Finucane, Romain Tessera

Let $(X_n)$ be an unbounded sequence of finite, connected, vertex transitive graphs such that $|X_n|=o(diam(X_n{)}^q)$ for some $q>0$. We show that up to taking a subsequence, an…