论文标题
不变合奏的派生原理
Derivative principles for invariant ensembles
论文作者
论文摘要
在目前的工作中，我们表明特征值的联合概率分布可以用作用于其他一些矩阵数量的分布的差分操作员表示。这些数量可能是对角线或伪 - 二角形条目，因为对于赫米尔式矩阵就是这种情况。这些表示称为衍生原理。我们向它们展示了Hermitian，Hermitian抗对称性，Hermitian抗二极管和复杂的矩形矩阵的添加空间，以及阳性确定的Hermitian矩阵的两个乘数基质空间和单位原始代表。在所有六种情况下，我们都证明了衍生原则的独特性。
In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential operator acting on the distribution of some other matrix quantities. Those quantities might be the diagonal or pseudo-diagonal entries as it is the case for Hermitian matrices. These representations are called derivative principles. We show them for the additive spaces of the Hermitian, Hermitian antisymmetric, Hermitian anti-self-dual, and complex rectangular matrices as well as for the two multiplicative matrix spaces of the positive definite Hermitian matrices and of the unitary matrices. In all six cases we prove the uniqueness of the derivative principles.
