Displaying similar documents to “On the spectral norm of a random Toeplitz matrix.”

Perturbed Toeplitz operators and radial determinantal processes

Torsten Ehrhardt, Brian Rider (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criterion for a central limit theorem to hold for angular statistics of the points. The proof exploits an exact formula relating the generating function of such statistics to the determinant of a perturbed Toeplitz matrix.

On Bernoulli decomposition of random variables and recent various applications

François Germinet (2007-2008)

Séminaire Équations aux dérivées partielles

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In this review, we first recall a recent Bernoulli decomposition of any given non trivial real random variable. While our main motivation is a proof of universal occurence of Anderson localization in continuum random Schrödinger operators, we review other applications like Sperner theory of antichains, anticoncentration bounds of some functions of random variables, as well as singularity of random matrices.

The asymptotic trace norm of random circulants and the graph energy

Sergiy Koshkin (2016)

Discussiones Mathematicae Probability and Statistics

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We compute the expected normalized trace norm (matrix/graph energy) of random symmetric band circulant matrices and graphs in the limit of large sizes, and obtain explicit bounds on the rate of convergence to the limit, and on the probabilities of large deviations. We also show that random symmetric band Toeplitz matrices have the same limit norm assuming that their band widths remain small relative to their sizes. We compare the limit norms across a range of related random matrix and...