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Perturbed Toeplitz operators and radial determinantal processes

Ehrhardt, T
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Rider, B
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Journal Article
Date
2013-11-01
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Subject
Random matrices
 Determinantal processes
 Toeplitz operators
 Szego-Widom limit theorem
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http://hdl.handle.net/20.500.12613/5931
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euclid.aihp.1380718732.pdf
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DOI
10.1214/12-AIHP501
Abstract
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. © Association des Publications de l'Institut Henri Poincaré, 2013.
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Institute of Mathematical Statistics
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Annales de l'institut Henri Poincare (B) Probability and Statistics
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