Nishigaki Shinsuke M
Graduate School of Science and Engineering, Shimane University, Matsue 690-8504, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 1):062102. doi: 10.1103/PhysRevE.86.062102. Epub 2012 Dec 6.
Schierenberg et al. [Phys. Rev. E 85, 061130 (2012)] recently applied the Wigner surmise, i.e., substitution of ∞ × ∞ matrices by their 2 × 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 Nyström-type method for the Fredholm determinant. The surmised expression at the best-fitting parameter provides a good approximation for 0 </~ s </~ 2, i.e., the validity range of the original surmise.
席伦贝格等人[《物理评论E》85, 061130 (2012年)]最近将维格纳推测，即在计算能级间距分布时用2 × 2矩阵替代无穷×无穷矩阵，应用于处于两个普适类之间转变的随机矩阵系综。我通过将其与我使用用于弗雷德霍姆行列式的奈斯特罗姆型方法评估的大N结果进行对比，研究了高斯正交系综和酉系综之间交叉的推测的准确性和有效性范围。在最佳拟合参数下的推测表达式对于0 </~ s </~ 2，即原始推测的有效性范围，提供了一个很好的近似。
