稀疏带状随机矩阵：特征函数的标度行为和谱性质
Diluted banded random matrices: Scaling behavior of eigenfunction and spectral properties
摘要：
我们证明了稀释（稀疏）带状随机矩阵的本征函数的归一化本地化长度$β$遵循标度律$β=x^*/(1+x^*)$。模型的缩放参数定义为$x^*\propto(b_{eff}^2/N)^δ$，其中$b_{eff}$是每个矩阵行的非零元素的平均数量，$N$是矩阵大小，以及$δ\sim 1$。此外，我们表明，$x^*$也规模的光谱特性的模型（达到一定的稀疏性）的特征值的间距分布。
英文摘要：
We demonstrate that the normalised localization length $β$ of the eigenfunctions of diluted (sparse) banded random matrices follows the scaling law $β=x^*/(1+x^*)$. The scaling parameter of the model is defined as $x^*\propto(b_{eff}^2/N)^δ$, where $b_{eff}$ is the average number of non-zero elements per matrix row, $N$ is the matrix size, and $δ\sim 1$. Additionally, we show that $x^*$ also scales the spectral properties of the model (up to certain sparsity) characterized by the spacing distribution of eigenvalues.
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