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• W2808831420 abstract "In this paper we establish eigenvector delocalization and bulk universality for Levy matrices, which are real, symmetric, $N times N$ random matrices $textbf{H}$ whose upper triangular entries are independent, identically distributed $alpha$-stable laws. First, if $alpha in (1, 2)$ and $E in mathbb{R}$ is any energy bounded away from $0$, we show that every eigenvector of $textbf{H}$ corresponding to an eigenvalue near $E$ is completely delocalized and that the local spectral statistics of $textbf{H}$ around $E$ converge to those of the Gaussian Orthogonal Ensemble (GOE) as $N$ tends to $infty$. Second, we show for almost all $alpha in (0, 2)$, there exists a constant $c(alpha) > 0$ such that the same statements hold if $|E| < c (alpha)$." @default.
• W2808831420 created "2018-06-29" @default.
• W2808831420 creator A5016887361 @default.
• W2808831420 creator A5072289328 @default.
• W2808831420 creator A5074069507 @default.
• W2808831420 date "2018-06-19" @default.
• W2808831420 modified "2023-10-18" @default.
• W2808831420 title "GOE Statistics for Levy Matrices" @default.
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