Product Matrix Processes as Limits of Random Plane Partitions
Product Matrix Processes as Limits of Random Plane Partitions
复制标题
DOI：
10.1093/imrn/rny297
复制
发表时间：
2018-06
影响因子：
1
通讯作者：
A. Borodin;V. Gorin;E. Strahov
中科院分区：
文献类型：
--
作者：
A. Borodin;V. Gorin;E. Strahov
考虑一类由Haar分布酉矩阵截尾乘积的平方奇异值构成的离散时间随机过程。我们表明，这个过程可以被理解为一个缩放限制的舒尔过程，它给出了（动态）相关函数和轮廓积分表示的相关内核的行列式公式。与Schur过程的关系意味着q-分布平面剖分的边缘的连续极限与Haar-分布随机酉矩阵截断乘积的奇异值平方的联合律一致。我们提供这种巧合的结构原因，也可以扩展到其他类别的随机矩阵。
We consider a random process with discrete time formed by squared singular values of products of truncations of Haar-distributed unitary matrices. We show that this process can be understood as a scaling limit of the Schur process, which gives determinantal formulas for (dynamical) correlation functions and a contour integral representation for the correlation kernel. The relation with the Schur processes implies that the continuous limit of marginals for q-distributed plane partitions coincides with the joint law of squared singular values for products of truncations of Haar-distributed random unitary matrices. We provide structural reasons for this coincidence that may also extend to other classes of random matrices.