The circular law for random regular digraphs with random edge weights

We consider random [Formula: see text] matrices of the form [Formula: see text], where [Formula: see text] is the adjacency matrix of a uniform random [Formula: see text]-regular directed graph on [Formula: see text] vertices, with [Formula: see text] for some fixed [Formula: see text], and [Formula: see text] is an [Formula: see text] matrix of i.i.d. centered random variables with unit variance and finite [Formula: see text]th moment (here ∘ denotes the matrix Hadamard product). We show that as [Formula: see text], the empirical spectral distribution of [Formula: see text] converges weakly in probability to the normalized Lebesgue measure on the unit disk.