Local deformed semicircle law and complete delocalization for Wigner matrices with random potential
Local deformed semicircle law and complete delocalization for Wigner matrices with random potential
复制标题
具有随机势的维格纳矩阵的局部变形半圆定律和完全离域
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Kevin Schnelli
中科院分区：
文献类型：
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作者：
J. Lee;Kevin Schnelli
我们考虑形式为$H=W+lambda V$的Hermite随机矩阵，其中$W$是Wigner矩阵，$V$是独立于$W$的对角随机矩阵。我们假设$W$的矩阵项的次指数衰减，并且我们选择$lambda sim 1$，使得$W$和$lambda V$的特征值在大部分频谱中具有相同的阶数。本文证明了对于一大类对角矩阵$V$，局部变形半圆律对$H$成立，这是一个类似于Wigner矩阵的局部变形半圆律的结果。我们还证明了特征向量的完全离域以及关于特征值位置的其他结果。
We consider Hermitian random matrices of the form $H = W + lambda V$, where $W$ is a Wigner matrix and $V$ a diagonal random matrix independent of $W$. We assume subexponential decay for the matrix entries of $W$ and we choose $lambda sim 1$ so that the eigenvalues of $W$ and $lambda V$ are of the same order in the bulk of the spectrum. In this paper, we prove for a large class of diagonal matrices $V$ that the local deformed semicircle law holds for $H$, which is an analogous result to the local semicircle law for Wigner matrices. We also prove complete delocalization of eigenvectors and other results about the positions of eigenvalues.
影响因子：
3.1
作者：
Erdos, Laszlo;Schlein, Benjamin;Yau, Horng-Tzer
通讯作者：
Yau, Horng-Tzer