Perturbed Toeplitz operators and radial determinantal processes

2011/02/14 by Torsten Ehrhardt, Ehrhardt, Torsten, Brian Rider +1
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Functional Analysis (math.FA) #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #math.FA #math.PR

paper · pdf · doi:10.48550/arxiv.1102.2682

35 pages

arxiv created 2011/02/14 · openalex publication_date 2011/02/14 · arxiv updated 2011/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 criteria 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.

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