2023/04/25 by Ratul Biswas, Arnab Sen, Biswas, Ratul +1
Mathematics · Medicine · #47H40 #60B20 #60E07 #60G57 #Advanced Algebra and Geometry #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2304.12564
openalex publication_date 2023/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an N × N random symmetric Toeplitz matrix with an i.i.d. input sequence drawn from a distribution that lies in the domain of attraction of an α-stable law for 0 < α< 2. We show that under an appropriate scaling, its empirical eigenvalue distribution, as N → ∞, converges weakly to a random symmetric probability distribution on ℝ, which can be described as the expected spectral measure of a certain random unbounded self-adjoint operator on ℓ2(ℤ). The limiting distribution turns out to be almost surely subgaussian. Furthermore, the support of the limiting distribution is bounded almost surely if 0<α<1 and is unbounded almost surely if 1≤ α<2.