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- W2896976107 abstract "The recent paper ``Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices'' by G. S. Dhesi and M. Ausloos [Phys. Rev. E 93, 062115 (2016)] uses the replica method to compute the $1/N$ correction to the Wigner semicircle law for the ensemble of real symmetric random matrices with 0's down the diagonal, and upper triangular entries independently chosen from the values $ifmmodepmelsetextpmfi{}w$ with equal probability. We point out that the results obtained are inconsistent with known results in the literature, as well as with known large $N$ series expansions for the trace of powers of these random matrices. An incorrect assumption relating to the role of the diagonal terms at order $1/N$ appears to be the cause for the inconsistency. Moreover, results already in the literature can be used to deduce the $1/N$ correction to the Wigner semicircle law for real symmetric random matrices with entries drawn independently from distributions ${mathcal{D}}_{1}$ (diagonal entries) and ${mathcal{D}}_{2}$ (upper triangular entries) assumed to be even and have finite moments. Large $N$ expansions for the trace of the $2kmathrm{th}$ power $(k=1,2,3)$ for these matrices can be computed and used as checks." @default.
- W2896976107 created "2018-10-26" @default.
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- W2896976107 date "2019-03-15" @default.
- W2896976107 modified "2023-09-27" @default.
- W2896976107 title "Comment on “Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices”" @default.
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- W2896976107 doi "https://doi.org/10.1103/physreve.99.036101" @default.
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