Extension of the limiting free-energy theorem beyond symmetric disorder

Let $\mathcal{D}$ be the distribution of the disorder random variable, and suppose that it has finite second moment. Throughout the paper the disorder is assumed to be symmetric, which is used to control the mean and covariance of off-diagonal entries of $A_N^{-1}$. Extension conjecture. Theorem holds for any distribution $\mathcal{D}$ with finite second moment. Numerical simulations suggest that the required asymptotic vanishing of the off-diagonal contributions may remain valid without the symmetry assumption, but this extension is not proved in the paper.