Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter
Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter
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拉盖尔和雅可比正交矩阵系综与参数的叠加和抽取的相关性
DOI：
10.1007/s00440-004-0374-7
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发表时间：
2002
影响因子：
2
通讯作者：
E. Rains
中科院分区：
文献类型：
--
作者：
P. Forrester;E. Rains
矩阵系综的叠加是指由原始系综的两个独立副本构造的系综，而抽取是指通过仅观察每隔一个特征值来形成新的系综。在具有正交对称性的经典矩阵系综的情况下，已知形成叠加和抽取会产生具有酉对称性和辛对称性的经典矩阵系综。表达这些事实的基本恒等式可以扩展为包含一个参数，这反过来又为我们提供了概率密度函数，我们将其作为特殊参数依赖矩阵系综的定义。与叠加相关的参数相关系综在叠加的正交系综和酉系综之间插值，而与抽取相关的参数相关系综在具有偶数个特征值的正交系综和具有一半特征值的辛系综之间进行插值。通过构建新的双正交和斜正交多项式族，我们能够在有限系统和各种标度极限下计算相应的相关函数。专门回到正交和辛对称的情况，我们发现我们的结果意味着与之前已知的不同的函数形式。
A superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original, while a decimation refers to the formation of a new ensemble by observing only every second eigenvalue. In the cases of the classical matrix ensembles with orthogonal symmetry, it is known that forming superpositions and decimations gives rise to classical matrix ensembles with unitary and symplectic symmetry. The basic identities expressing these facts can be extended to include a parameter, which in turn provides us with probability density functions which we take as the definition of special parameter dependent matrix ensembles. The parameter dependent ensembles relating to superpositions interpolate between superimposed orthogonal ensembles and a unitary ensemble, while the parameter dependent ensembles relating to decimations interpolate between an orthogonal ensemble with an even number of eigenvalues and a symplectic ensemble of half the number of eigenvalues. By the construction of new families of biorthogonal and skew orthogonal polynomials, we are able to compute the corresponding correlation functions, both in the finite system and in various scaled limits. Specializing back to the cases of orthogonal and symplectic symmetry, we find that our results imply different functional forms to those known previously.
Whittaker 向量的空间不可约性
DOI：
--
发表时间：
2007
期刊：
影响因子：
--
作者：
Ikehata;M and Ohe;T;松本久義
通讯作者：
松本久義