ALMOST HERMITIAN RANDOM MATRICES : CROSSOVER FROM WIGNER-DYSON TO GINIBRE EIGENVALUE STATISTICS
ALMOST HERMITIAN RANDOM MATRICES : CROSSOVER FROM WIGNER-DYSON TO GINIBRE EIGENVALUE STATISTICS
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几乎 Hermitian 随机矩阵：从 WIGNER-DYSON 到 GINIBRE 特征值统计的交叉
DOI：
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发表时间：
1997
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通讯作者：
H. Sommers
中科院分区：
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作者：
Y. Fyodorov;B. Khoruzhenko;H. Sommers
本文利用正交多项式的方法，分析了随机矩阵复特征值的统计性质，该随机矩阵的复特征值是从实数特征值的Wigner-Dyson统计特征值表征的厄米矩阵到Ginibre研究的复特征值的强非厄米矩阵的交叉。更详细地研究了两点统计度量[例如，光谱形状因子、数量方差和最近邻距离分布p(s)的小距离行为]。特别是，我们发现后一个函数对于某些参数值可能表现出不寻常的行为p(s){proporal_to}s{sup 5/2}。{版权所有}{ital 1997} {ital美国物理学会}
By using the method of orthogonal polynomials, we analyze the statistical properties of complex eigenvalues of random matrices describing a crossover from Hermitian matrices characterized by the Wigner-Dyson statistics of real eigenvalues to strongly non-Hermitian ones whose complex eigenvalues were studied by Ginibre. Two-point statistical measures [as, e.g., spectral form factor, number variance, and small distance behavior of the nearest neighbor distance distribution p(s) ] are studied in more detail. In particular, we found that the latter function may exhibit unusual behavior p(s){proportional_to}s{sup 5/2} for some parameter values. {copyright} {ital 1997} {ital The American Physical Society}