Comment on "Finite size effects in the averaged eigenvalue density ofWigner random-sign real symmetric matrices"
Peter J Forrester, Allan K Trinh
PHYSICAL REVIEW E | AMER PHYSICAL SOC | Published : 2019
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)10.1103/PhysRevE.93.062115] 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 ±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..View full abstract
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Awarded by ARC
This work is part of a research program supported by the Australian Research Council (ARC) through the ARC Centre of Excellence for Mathematical and Statistical frontiers (ACEMS). P.J.F. also acknowledges partial support from ARC Grant No. DP170102028, and A.K.T. acknowledges the support of a Melbourne postgraduate award.