On the lower bound of the spectral norm of symmetric random matrices with independent entries

dc.creatorPeche, Sandrine
dc.creatorSoshnikov, Alexander
dc.date2007-06-06
dc.date2008-05-13
dc.date.accessioned2026-07-07T09:38:07Z
dc.date.available2026-07-07T09:38:07Z
dc.descriptionWe show that the spectral radius of an $N\times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from below by $ 2 \*σ- o(N^{-6/11+ε}), $ where $σ^2 $ is the variance of the matrix entries and $ε$ is an arbitrary small positive number. Combining with our previous result from [7], this proves that for any $ε>0, $ one has $$ \|A_N\| =2 \*σ+ o(N^{-6/11+ε}) $$ with probability going to 1 as $N \to \infty. $
dc.identifierhttps://arxiv.org/abs/0706.0748
dc.identifierhttp://arxiv.org/abs/0706.0748
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160691
dc.subjectProbability
dc.subjectCombinatorics
dc.titleOn the lower bound of the spectral norm of symmetric random matrices with independent entries
dc.typetext

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