标题： 具有分裂极限行为的随机矩阵系综 显示英文标题

标题： Random Matrix Ensembles with Split Limiting Behavior

摘要： 我们引入了一类新的$N\times N$随机实对称矩阵系，即$k$棋盘矩阵，其极限谱测度有两个组成部分，可以显式确定。 几乎所有$k$个特征值都在主体中，经过适当归一化后，它们的行为收敛到半圆分布当$N\to\infty$；其余的$k$个特征值紧密约束在$N/k$附近，其分布收敛到$k \times k$空心 GOE 系列 （这是通过将 GOE 系列中的所有主对角线元素强制为零而得到的密度）。 类似的结果也适用于复数和四元数的类似情况。 我们通过使用矩阵扰动结果和特征值的非标准权重函数来区分这两个区域，然后通过修改矩方法并分析由此产生的组合学来推导它们的极限分布。 显示英文摘要

摘要： We introduce a new family of $N\times N$ random real symmetric matrix ensembles, the $k$-checkerboard matrices, whose limiting spectral measure has two components which can be determined explicitly. All but $k$ eigenvalues are in the bulk, and their behavior, appropriately normalized, converges to the semi-circle as $N\to\infty$; the remaining $k$ are tightly constrained near $N/k$ and their distribution converges to the $k \times k$ hollow GOE ensemble (this is the density arising by modifying the GOE ensemble by forcing all entries on the main diagonal to be zero). Similar results hold for complex and quaternionic analogues. We isolate the two regimes by using matrix perturbation results and a nonstandard weight function for the eigenvalues, then derive their limiting distributions using a modification of the method of moments and analysis of the resulting combinatorics.