Abstract
We consider the deformed Gaussian ensemble \(H_{n}=H_{n}^{(0)}+M_{n}\) in which \(H_{n}^{(0)}\) is a hermitian matrix (possibly random) and M n is the Gaussian unitary random matrix (GUE) independent of \(H_{n}^{(0)}\). Assuming that the Normalized Counting Measure of \(H_{n}^{(0)}\) converges weakly (in probability if random) to a non-random measure N (0) with a bounded support and assuming some conditions on the convergence rate, we prove the universality of the local eigenvalue statistics near the edge of the limiting spectrum of H n .
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Shcherbina, T. On Universality of Local Edge Regime for the Deformed Gaussian Unitary Ensemble. J Stat Phys 143, 455–481 (2011). https://doi.org/10.1007/s10955-011-0196-9
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DOI: https://doi.org/10.1007/s10955-011-0196-9