Hard edge limit of the product of two strongly coupled random matrices
Hard edge limit of the product of two strongly coupled random matrices
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DOI：
10.1088/0951-7715/29/12/3743
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发表时间：
2016-12-01
期刊：
影响因子：
1.7
通讯作者：
Strahov, Eugene
中科院分区：
文献类型：
--
作者：
Akemann, Gernot;Strahov, Eugene
我们研究了由两个耦合复随机矩阵乘积的奇异值平方定义的系综的硬边标度极限。当耦合参数依赖于乘积矩阵的大小时，在原点处的一定双标度区域中，两个矩阵变得强耦合，并且我们获得了一个新的硬边限制核。它插值之间的经典贝塞尔核描述的硬边缩放限制的拉盖尔系综的一个矩阵，和Meijer G核Kuijlaars和张描述的硬边缩放限制的产品的两个独立的高斯复矩阵。它不同于我们比较的插值核Borodin。
We investigate the hard edge scaling limit of the ensemble defined by the squared singular values of the product of two coupled complex random matrices. When taking the coupling parameter to be dependent on the size of the product matrix, in a certain double scaling regime at the origin the two matrices become strongly coupled and we obtain a new hard edge limiting kernel. It interpolates between the classical Bessel-kernel describing the hard edge scaling limit of the Laguerre ensemble of a single matrix, and the Meijer G-kernel of Kuijlaars and Zhang describing the hard edge scaling limit for the product of two independent Gaussian complex matrices. It differs from the interpolating kernel of Borodin to which we compare as well.