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Perturbed Toeplitz operators and radial determinantal processes

Torsten EhrhardtBrian Rider — 2013

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

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.

Rank decomposition in zero pattern matrix algebras

Harm BartTorsten EhrhardtBernd Silbermann — 2016

Czechoslovak Mathematical Journal

For a block upper triangular matrix, a necessary and sufficient condition has been given to let it be the sum of block upper rectangular matrices satisfying certain rank constraints; see H. Bart, A. P. M. Wagelmans (2000). The proof involves elements from integer programming and employs Farkas' lemma. The algebra of block upper triangular matrices can be viewed as a matrix algebra determined by a pattern of zeros. The present note is concerned with the question whether the decomposition result referred...

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