Localization and delocalization of eigenvectors for heavy-tailed random matrices
Localization and delocalization of eigenvectors for heavy-tailed random matrices
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DOI：
10.1007/s00440-012-0473-9
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发表时间：
2013-12-01
影响因子：
2
通讯作者：
Guionnet, Alice
中科院分区：
文献类型：
--
作者：
Bordenave, Charles;Guionnet, Alice
考虑一个厄米特随机矩阵，其对角线上的元素独立，且具有-稳定的对称分布和。我们建立了新的边界上的收敛速度的经验谱分布的随机矩阵走向无穷大。当和时，我们给出了特征向量的单位范数的零界.相反，当，我们证明了这些特征向量是局部的。
Consider an Hermitian random matrix with, above the diagonal, independent entries with -stable symmetric distribution and . We establish new bounds on the rate of convergence of the empirical spectral distribution of this random matrix as goes to infinity. When and , we give vanishing bounds on the -norm of the eigenvectors normalized to have unit -norm. On the contrary, when , we prove that these eigenvectors are localized.