  We analyze the macroscale behavior of random lower (and therefore upper)
triangular matrices with entries drawn iid from a distribution with nonzero
mean and finite variance. We show that such a matrix behaves like a
probabilistic version of a Riemann sum and therefore in the limit behaves like
the Volterra operator. Specifically, we analyze certain SOT-like and WOT-like
modes of convergence for random lower triangular matrices to a scaled Volterra
operator. We close with a brief discussion of moments.
