Limits of random trees

Local convergence of bounded degree graphs was introduced by Benjamini and Schramm 2]. This result was extended further by Lyons 4] to bounded average degree graphs. In this paper, we study the convergence of a random tree sequence (T _n ), where the probability of a given tree T is proportional to $\prod_{v_{i}\in V(T)}d(v_{i})!$ . We show that this sequence is convergent and describe the limit object, which is a random infinite rooted tree.