Perturbed Toeplitz operators and radial determinantal processes
Probability
2011-02-15 v1 Functional Analysis
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.
Cite
@article{arxiv.1102.2682,
title = {Perturbed Toeplitz operators and radial determinantal processes},
author = {Torsten Ehrhardt and Brian Rider},
journal= {arXiv preprint arXiv:1102.2682},
year = {2011}
}
Comments
35 pages