Ji Oon Lee, Kevin Schnelli
We consider random matrices of the form $H = W + \lambda V$, where $W$ is a Wigner matrix and $V$ a random diagonal matrix. 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.
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http://arxiv.org/abs/1302.4532
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