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Samuel Modée: Limiting Behavior of the Largest Eigenvalues of Random Toeplitz Matrices

Time: Wed 2019-11-20 13.00 - 14.00

Location: KTH, F11

Participating: Samuel Modée


The subject of my talk is random symmetric Toeplitz matrices of size n. Assuming that the distinct entries are independent centered random variables with finite \(\gamma\)-th moment (\(\gamma>2\)), I will establish a law of large numbers for the largest eigenvalue. Following the approach of Sen and Virág (2013), in the large \(n\) limit, the largest eigenvalue rescaled by \(\sqrt{2n\, log(n)}\) is shown to converge to the limit \(0.8288...\) . I will explain the background theory and also present some related results. Finally, a numerical analysis is used to illustrate the rate of convergence and the oscillatory nature of the eigenvectors of random Toeplitz matrices.