CONVERGENCE OF A CLASS OF TOEPLITZ TYPE MATRICES

We use the method of moments to study the spectral properties in the bulk for finite diagonal large dimensional random and non-random Toeplitz type matrices via the joint convergence of matrices in an appropriate sense. As a consequence we revisit the famous limit theorem of Szegö for non-random symmetric Toeplitz matrices.

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Algebraic and Spectral Properties of General Toeplitz Matrices

SIAM Journal on Control and Optimization ◽

10.1137/s0363012900377183 ◽

2002 ◽

Vol 41 (5) ◽

pp. 1413-1439 ◽

Cited By ~ 8

Author(s):

A. Bultheel ◽

P. Carrette

Keyword(s):

Spectral Properties ◽

Toeplitz Matrices

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An observation on certain spectral properties of Toeplitz matrices

CALCOLO ◽

10.1007/bf02575868 ◽

1991 ◽

Vol 28 (1-2) ◽

pp. 37-43 ◽

Cited By ~ 2

Author(s):

D. Bini ◽

F. Di Benedetto

Keyword(s):

Spectral Properties ◽

Toeplitz Matrices

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SPECTRAL PROPERTIES OF CHAOTIC PROCESSES

Stochastics and Dynamics ◽

10.1142/s0219493706001785 ◽

2006 ◽

Vol 06 (03) ◽

pp. 355-371

Author(s):

BERNARD BERCU ◽

CLÉMENTINE PRIEUR

Keyword(s):

Dynamical System ◽

Limit Theorem ◽

Spectral Properties ◽

Law Of Large Numbers ◽

Fourier Transforms ◽

Asymptotic Properties ◽

Initial State ◽

Strong Law ◽

Expanding Map ◽

Large Numbers

We investigate the spectral asymptotic properties of the stationary dynamical system ξt= φ(Tt(X0)). This process is given by the iterations of a piecewise expanding map T of the interval [0,1], invariant for an ergodic probability μ. The initial state X0is distributed over [0,1] according to μ and φ is a function taking values in ℝ. We establish a strong law of large numbers and a central limit theorem for the integrated periodogram as well as for Fourier transforms associated with (ξt: t ∈ ℕ). Several examples of expanding maps T are also provided.

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Asymptotics of determinants of block Toeplitz matrices

Random Matrices Theory and Application ◽

10.1142/s2010326317400032 ◽

2017 ◽

Vol 06 (04) ◽

pp. 1740003 ◽

Cited By ~ 1

Author(s):

Estelle Basor

Keyword(s):

Limit Theorem ◽

Toeplitz Matrices ◽

Constant Term ◽

Scalar Case ◽

Block Toeplitz Matrices

This paper is a survey of results that show how, in some cases, to compute the constant term which occurs in the Strong Szegö–Widom Limit Theorem for block Toeplitz matrices. While this constant in the scalar case has a long history, it is really only in a few instances that it can be calculated explicitly in the case of matrix-valued symbols.

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