Bulk universality for deformed Wigner matrices
The authors consider \(N\times N\) random matrices of the form \(H=W+V\) where \(W\) is a real symmetric or complex Hermitian Wigner matrix and \(V\) is a random or deterministic real diagonal matrix whose entries are independent of \(W\). Subexponential decay for the matrix entries of \(W\) is assumed, and \(V\) is chosen so that the eigenvalues of \(W\) and \(V\) are typically of the same order. For a large class of diagonal matrices \(V\), it is shown that the local statistics in the bulk of the spectrum are universal in the limit of large \(N\).
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