Proves local laws comparing the spectrum of H = W + λV to a refined deformed semicircle law, plus rigidity and asymptotic normality of extremal eigenvalues under mild assumptions on entries.
O., Schnelli, K.: Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices , Probab
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Local laws and spectral properties of deformed sparse random matrices
Proves local laws comparing the spectrum of H = W + λV to a refined deformed semicircle law, plus rigidity and asymptotic normality of extremal eigenvalues under mild assumptions on entries.