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Journal articles
Delocalization at small energy for heavy-tailed random matrices
Abstract : We prove that the eigenvectors associated to small enough eigenvalues of an 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.
Cited literature [25 references]
https://hal-ens-lyon.archives-ouvertes.fr/ensl-01655012
Contributor : Alice Guionnet <>
Submitted on : Monday, December 4, 2017 - 3:26:38 PM
Last modification on : Monday, December 14, 2020 - 6:12:40 PM
Contributor : Alice Guionnet <>
Submitted on : Monday, December 4, 2017 - 3:26:38 PM
Last modification on : Monday, December 14, 2020 - 6:12:40 PM
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deloc_loilocale_rev.pdf
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