Skip to Main content Skip to Navigation
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.
Document type :
Journal articles
Complete list of metadata

Cited literature [25 references]  Display  Hide  Download
Contributor : Alice Guionnet Connect in order to contact the contributor
Submitted on : Monday, December 4, 2017 - 3:26:38 PM
Last modification on : Monday, July 4, 2022 - 10:27:35 AM


Files produced by the author(s)


  • HAL Id : ensl-01655012, version 1


Charles Bordenave, Alice Guionnet. Delocalization at small energy for heavy-tailed random matrices. Communications in Mathematical Physics, Springer Verlag, 2017, 354, pp.115-159. ⟨ensl-01655012⟩



Record views


Files downloads