Mathematics – Probability
Scientific paper
2011-02-14
Mathematics
Probability
35 pages
Scientific paper
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.
Ehrhardt Torsten
Rider Brian
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