Limiting spectral distributions of self-adjoint nonWigner random matrix ensembles with conditionally independent rows

Abstract

We explore limiting spectral distributions of self-adjoint nonWigner random matrices with conditional independence between entries in a row. We investigate the case where the partial sums of a row converge to a mixture of infinitely divisible distributions. Based on the results in the independent case, we extend the results to show that the spectral measures of the unit vector at a fixed vertex converges to the spectral measure of a mixed form of a Poisson-weighted infinite trees at its root vector. We construct local weak convergence of the associated adjacency operators and upgrade it to strong resolvent convergence, which imlies convergence of the probability measures in the weak topology. The mixture corresponds exactly to the mixture that appears in the limiting distributions of sums of a row.