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• W2331892397 abstract "We prove that the eigenvectors associated to small enough eigenvalues of a heavy-tailed symmetric random matrix are delocalized with probability tending to one as the size of the matrix grows to infinity. The delocalization is measured thanks to a simple criterion related to the inverse participation ratio which computes an average ratio of $${L^4}$$ and $${L^2}$$ -norms of vectors. In contrast, as a consequence of a previous result, for random matrices with sufficiently heavy tails, the eigenvectors associated to large enough eigenvalues are localized according to the same criterion. The proof is based on a new analysis of the fixed point equation satisfied asymptotically by the law of a diagonal entry of the resolvent of this matrix." @default.
• W2331892397 created "2016-06-24" @default.
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• W2331892397 date "2017-05-23" @default.
• W2331892397 modified "2023-10-09" @default.
• W2331892397 title "Delocalization at Small Energy for Heavy-Tailed Random Matrices" @default.
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• W2331892397 doi "https://doi.org/10.1007/s00220-017-2914-x" @default.
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