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首页> 外文期刊>Physical review, E >Comment on 'Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices'
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Comment on 'Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices'

机译：评论“有限尺寸效应在Wigner随机符号真实对称矩阵的平均特征值密度”

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摘要

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 ±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 D_1 (diagonal entries) and D_2 (upper triangular entries) assumed to be even and have finite moments. Large N expansions for the trace of the 2kth power (k = 1, 2, 3) for these matrices can be computed and used as checks.
机译：最近的纸张“在Wigner随机符号真实对称矩阵的平均特征密度的有限尺寸效应”由G.S. Dhesi和M. ausloos [phys。 Rev. E 93,062115（2016）]使用副本方法计算到Wigner半圆法的Wigner半圆定律，用于使用0下沿对角线的实际对称随机矩阵的集合，以及独立从值中选择的上三角条目± w具有相同的概率。我们指出，所获得的结果与文献中的已知结果不一致，以及用于这些随机矩阵的迹线的已知大n系列扩展。与订单1 / n处的对角线术语的角色有关的错误假设似乎是不一致的原因。此外，已经在文献中的结果可以用于向Wigner半圆法向Wigner半圆法向实际对称随机矩阵推导出来，其中具有从分布D_1（对角线条目）和D_2（上三角条目）被假定为偶数和有有限的时刻。可以计算用于这些矩阵的第2次电源（k = 1,2,3）的轨迹的大n扩展，并用作检查。

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