随机矩阵理论中混合对称类的Wigner曲面的精度和有效范围
Accuracy and range of validity of the Wigner surmise for mixed symmetry classes in random matrix theory
摘要：
Schierenberg等人[Phys.Rev.E85，061130（2012）]最近应用了维格纳表面，即，将\infty \times \infty矩阵替换为用于计算能级间距分布的2个\times 2对应矩阵，以在两个普适类之间过渡的随机矩阵系综。我检查的准确性和范围的有效性的surrounds的交叉之间的高斯正交和酉系综，通过对比它们与大N的结果，我使用Nystrom型方法的Fredholm行列式评估。在最佳拟合参数处的推测表达式提供了0 \lesssim s \lesssim 2的良好近似，即，原附随书的有效范围。
英文摘要：
Schierenberg et al. [Phys. Rev. E 85, 061130 (2012)] recently applied the Wigner surmise, i.e., substitution of \infty \times \infty matrices by their 2 \times 2 counterparts for the computation of level spacing distributions, to random matrix ensembles in transition between two universality classes. I examine the accuracy and the range of validity of the surmise for the crossover between the Gaussian orthogonal and unitary ensembles by contrasting them with the large-N results that I evaluated using the Nystrom-type method for the Fredholm determinant. The surmised expression at the best-fitting parameter provides a good approximation for 0 \lesssim s \lesssim 2, i.e., the validity range of the original surmise.
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