Electronic Communications in Probability

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

Sandrine Peche and Alexander Soshnikov

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Abstract

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 \sigma - o( N^{-6/11+\varepsilon}), $ where $\sigma^2 $ is the variance of the matrix entries and $\varepsilon $ is an arbitrary small positive number. Combining with our previous result from [7], this proves that for any $\varepsilon <0, \ $ one has $ \|A_N\| =2 \sigma + o( N^{-6/11+\varepsilon}) $ with probability going to $ 1 $ as $N \to \infty$.

Article information

Source
Electron. Commun. Probab., Volume 13 (2008), paper no. 28, 280-290.

Dates
Accepted: 1 June 2008
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465233455

Digital Object Identifier
doi:10.1214/ECP.v13-1376

Mathematical Reviews number (MathSciNet)
MR2415136

Zentralblatt MATH identifier
1189.15046

Subjects
Primary: 15A52
Secondary: 60C05: Combinatorial probability

Keywords
Wigner random matrices spectral norm

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Peche, Sandrine; Soshnikov, Alexander. On the lower bound of the spectral norm of symmetric random matrices with independent entries. Electron. Commun. Probab. 13 (2008), paper no. 28, 280--290. doi:10.1214/ECP.v13-1376. https://projecteuclid.org/euclid.ecp/1465233455


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