On the lower bound of the spectral norm of symmetric random matrices with independent entries
| dc.creator | Peche, Sandrine | |
| dc.creator | Soshnikov, Alexander | |
| dc.date | 2007-06-06 | |
| dc.date | 2008-05-13 | |
| dc.date.accessioned | 2026-07-07T09:38:07Z | |
| dc.date.available | 2026-07-07T09:38:07Z | |
| dc.description | We 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.identifier | https://arxiv.org/abs/0706.0748 | |
| dc.identifier | http://arxiv.org/abs/0706.0748 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160691 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.title | On the lower bound of the spectral norm of symmetric random matrices with independent entries | |
| dc.type | text |