Spectral norm of random Toeplitz matrices

2013/01/05 by Malika Kharouf, Kharouf, Malika
Mathematics · #15A18 #60F05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1301.0938

openalex publication_date 2013/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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|X₁|ⁿ ≤ n^√(n) for all n≥ 3. We prove that the largest eigenvalue of T_n scaled by √(n log(n)) converges almost surely to 1.

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