Transitive ensembles of random matrices related to orthogonal polynomials
Transitive ensembles of random matrices related to orthogonal polynomials
复制标题
与正交多项式相关的随机矩阵的传递系综
DOI：
10.1016/s0550-3213(98)00501-x
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
P. Forrester
中科院分区：
文献类型：
--
作者：
T. Nagao;P. Forrester
研究了介于真实的对称与埃尔米特、自对偶四元数与埃尔米特、反对称与埃尔米特之间的随机矩阵系综特征值的传递相关性。对于与一般正交多项式相关的随机矩阵系综，得到了精确的n点相关函数的表达式。在大矩阵维数的极限下，在谱边缘处，对与勒让德多项式有关的系综，给出了渐近公式。所得结果插值了已知的随机矩阵特征值的渐近公式。
Transitive correlations of eigenvalues for random matrix ensembles intermediate between real symmetric and hermitian, self-dual quaternion and hermitian, and antisymmetric and hermitian are studied. Expressions for exact n-point correlation functions are obtained for random matrix ensembles related to general orthogonal polynomials. The asymptotic formulas in the limit of large matrix dimension are evaluated at the spectrum edges for the ensembles related to the Legendre polynomials. The results interpolate known asymptotic formulas for random matrix eigenvalues.