论文标题
周期性的雅各比矩阵的周期性边界条件
Periodic Boundary Conditions for Periodic Jacobi Matrices on Trees
论文作者
论文摘要
我们认为无限树上的矩阵是有限图上的雅各比矩阵的通用覆盖物。我们对存在有限覆盖序列的存在的问题感兴趣，这些序列的归一化特征值计数措施融合到无限树上操作员状态的密度。首先，我们构建了一个简单的示例，其中这种收敛失败，然后讨论构造所需序列的两种方法：使用随机边界条件和正常亚组。
We consider matrices on infinite trees which are universal covers of Jacobi matrices on finite graphs. We are interested in the question of the existence of sequences of finite covers whose normalized eigenvalue counting measures converge to the density of states of the operator on the infinite tree. We first of all construct a simple example where this convergence fails and then discuss two ways of constructing the required sequences: with random boundary conditions and through normal subgroups.
