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- W2951569105 abstract "In this paper we consider $N times N$ real generalized Wigner matrices whose entries are only assumed to have finite $(2 + varepsilon)$-th moment for some fixed, but arbitrarily small, $varepsilon > 0$. We show that the Stieltjes transforms $m_N (z)$ of these matrices satisfy a weak local semicircle law on the nearly smallest possible scale, when $eta = Im (z)$ is almost of order $N^{-1}$. As a consequence, we establish bulk universality for local spectral statistics of these matrices at fixed energy levels, both in terms of eigenvalue gap distributions and correlation functions, meaning that these statistics converge to those of the Gaussian Orthogonal Ensemble (GOE) in the large $N$ limit." @default.
- W2951569105 created "2019-06-27" @default.
- W2951569105 creator A5016887361 @default.
- W2951569105 date "2016-12-01" @default.
- W2951569105 modified "2023-09-25" @default.
- W2951569105 title "Bulk Universality for Generalized Wigner Matrices With Few Moments" @default.
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