A sequence of random finite-volume manifolds X_i Benjamini-Schramm converges to a random pointed manifold (X,p) if, when p_i is a random point in X_i chosen uniformly, then the law of (X_i, p_i) converges to the law of (X, p) in the space of Borel probability measures on the space of pointed manifolds. This convergence notion admits natural generalizations to manifolds endowed with extra structures, such as abelian differentials. We will describe the Benjamini-Schramm limit of a random translation surface of genus g as g approaches infinity. This is a joint work in progress with Lewis Bowen and Hunter Vallejos.