论文标题
混合Wigner的确切差距结果可高达4个特征值
Exact gap-ratio results for mixed Wigner surmises of up to 4 eigenvalues
论文作者
论文摘要
我们计算了多达四个特征值和$ 0 \leqβ\ leq4 $的混合Wigner Surmises的间隙比例的确切结果。主要结果涉及GOE，GUE和GSE随机矩阵类的相等混合物。这些引起到$ 2 \ times $ goe，$ 2 \ times $ gue和$ 2 \ times $ gse〜发行版。我们发现分别只有2+2个特征值分别分发了2+2个特征值，$ 2 \ times $ goe，$ 2 \ times $ gue近似。同样的$ 2 \ times $ GSE无效，这是通过2+2特征值的统计数据中间的，这是GUE和GSE之间的2+2特征值。
We compute some exact results for the gap-ratio of mixed Wigner surmises for up to four eigenvalues and $0\leqβ\leq4$. The main results concern equal mixtures of the GOE, GUE, and GSE random matrix classes. These give rise to $2\times$GOE, $2\times$GUE, and $2\times$GSE~distributions. We find that $2\times$GOE, $2\times$GUE are well approximated by the surmises of only 2+2 eigenvalues that are GOE and GUE distributed, respectively. The same is not valid for $2\times$GSE, which is well estimated, by coincidence, by 2+2 eigenvalues of statistics intermediate between GUE and GSE.
