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The recent paper "Finite size effects in the averaged eigenvalue density ofWigner random-sign real symmetric matrices" by G.S. Dhesi and M. Ausloos [Phys.Rev. E 93 (2016), 062115] uses the replica method to compute the $1/N$correction to the Wigner semi-circle law for the ensemble of real symmetricrandom matrices with $0$'s down the diagonal, and upper triangular entriesindependently chosen from the values $\pm w$ with equal probability. We pointout that the results obtained are inconsistent with known results in theliterature, as well as with known large $N$ series expansions for the trace ofpowers of these random matrices. An incorrect assumption relating to the roleof the diagonal terms at order $1/N$ appears to be the cause for theinconsistency. Moreover, results already in the literature can be used todeduce the $1/N$ correction to the Wigner semi-circle law for real symmetricrandom matrices with entries drawn independently from distributions $\mathcalD_1$ (diagonal entries) and $\mathcal D_2$ (upper triangular entries) assumedto be even and have finite moments. Large $N$ expansions for the trace of the$2k$-th power ($k=1,2,3$) for these matrices can be computed and used aschecks.

Comment on "Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices" by G.S. Dhesi and M. Ausloos