Spectral norm of random Toeplitz matrices

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 $\sqrt{nlog(n)}$ converges almost surely to $1$.

This paper has been withdrawn by the author for improvement

References in corpus (2)

• Spectral measure of large random Hankel, Markov and Toeplitz matrices
• Eigenvalue Spacing Distribution for the Ensemble of Real Symmetric Toeplitz Matrices