Two coupled matrices: eigenvalue correlations and spacing functions
Two coupled matrices: eigenvalue correlations and spacing functions
复制标题
两个耦合矩阵：特征值相关性和间距函数
DOI：
--
复制
发表时间：
1994
期刊：
影响因子：
--
通讯作者：
P. Shukla
中科院分区：
文献类型：
--
作者：
M. L. Mehta;P. Shukla
对于两个n*n厄米矩阵A和B，联合概率密度正比于exp(- tr(U(A)+V(B)+2cAB))，其中U和V是多项式，给出了一种计算一个或两个矩阵特征值的所有相关函数、聚类函数和间隔函数的方法。该方法依赖于引入两组具有非局部权值的双正交多项式。在一个耦合矩阵的线性链中，如果我们寻找位于链中任意位置的一个矩阵（两个矩阵）的特征值的统计性质，那么我们可以将其作为一个单矩阵（两个矩阵）问题进行处理。
For two n*n Hermitian matrices A and B, with joint probability density proportional to exp(- tr(U(A)+V(B)+2cAB)), where U and V are polynomials, a method is given to calculate all correlation, cluster and spacing functions of the eigenvalues of either one or both matrices. The method relies on the introduction of two sets of bi-orthogonal polynomials with non-local weights. In a linear chain of coupled matrices, if one looks for the statistical properties of the eigenvalues of only one matrix (two matrices), situated anywhere in the chain, then we can proceed as a one-matrix (two-matrices) problem.