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

Alexander B. Soshnikov
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Abstract

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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Alexander B. Soshnikov. 1999-12-14. Gaussian fluctuation for the number of particles in Airy, Bessel, sine and other determinantal random point fields. https://arxiv.org/abs/math-ph/9907012

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