Péché, Sandrine; Soshnikov, Alexander On the lower bound of the spectral norm of symmetric random matrices with independent entries. (English) Zbl 1189.15046 Electron. Commun. Probab. 13, 280-290 (2008). Summary: We show that the spectral radius of an \(N\)-dimensional random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from below by \(2\sigma - o(N^{-6/11+\epsilon })\), where \(\sigma ^{2}\) is the variance of the matrix entries and \(\epsilon > 0\) is an arbitrary small positive number. Combining with our previous result from [J. Stat. Phys. 129, No. 5–6, 857–884 (2007; Zbl 1139.82019)], this proves that for any \(\varepsilon > 0\) one has \(\|A_{N}\| = 2\sigma + o(N^{-6/11+\varepsilon})\) with probability going to 1 as \(N\) goes to infinity. Cited in 12 Documents MSC: 15B52 Random matrices (algebraic aspects) 15A18 Eigenvalues, singular values, and eigenvectors 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory 60C05 Combinatorial probability Keywords:Wigner random matrices; spectral norm; spectral radius Citations:Zbl 1139.82019 × Cite Format Result Cite Review PDF Full Text: DOI arXiv EuDML EMIS Online Encyclopedia of Integer Sequences: Arises in lower bound of the spectral norm of n X n symmetric random matrices.