Gaussian fluctuation for the number of particles in Airy, Bessel, sine and other determinantal random point fields

Details Gaussian fluctuation for the number of particles in Airy, Bessel, sine and other determinantal random point fields Gaussian fluctuation for the number of particles in Airy, Bessel, sine and other determinantal random point fields

1999-07-15

arxiv.org/abs/math-ph/9907012v2

Physics

Mathematical Physics

The essential alterations are a slightly different formulation of the Costin-Lebowitz Theorem and the addition of Remark 4 in

Scientific paper

We prove the Central Limit Theorem for the number of eigenvalues near the spectrum edge for hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the Gaussian fluctuation of the number of particles in random point fields with determinantal correlation functions. As another corollary of Costin-Lebowitz Theorem we prove CLT for the empirical distribution function of the eigenvalues of random matrices from classical compact groups.

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