Spectral norm of random Toeplitz matrices

Malika Kharouf

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arXiv · 1301.0938

Spectral norm of random Toeplitz matrices

Malika Kharouf

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Abstract

In this work, we consider symmetric random Toeplitz matrices $T_n$ generated by i.i.d. zero mean random variables ${X_k}$ satisfying the moment conditions: $E|X_k|^2=1$ and $\E|X_1|^n \le n^{\sqrt{n}}$ for all $n\ge 3$. We prove that the largest eigenvalue of $T_n$ scaled by $\sqrt{n log(n)}$ converges almost surely to $1$.

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BibTeX RIS

Malika Kharouf. 2013-01-09. Spectral norm of random Toeplitz matrices. https://arxiv.org/abs/1301.0938

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