  We review the application of the notion of local convergence on locally
finite randomly rooted graphs, known as Benjamini-Schramm convergence, to the
calculation of the global eigenvalue density of random matrices from the
beta-Gaussian and beta-Laguerre ensembles. By regarding a random matrix as the
weighted adjacency matrix of a graph, and choosing the root of such a graph
with uniform probability, one can use the Benjamini-Schramm limit to produce
the spectral measure of the adjacency operator of the limiting graph. We
illustrate how the Wigner semicircle law and the Marchenko-Pastur law are
obtained from this machinery.
