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Gaussian Fluctuation for the Number of Particles in Airy, Bessel, Sine, and Other Determinantal Random Point Fields

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Abstract

We prove the Central Limit Theorem (CLT) for the number of eigenvalues near the spectrum edge for certain 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 the Costin–Lebowitz Theorem we prove the CLT for the empirical distribution function of the eigenvalues of random matrices from classical compact groups.

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Authors and Affiliations

  1. Department of Mathematics, California Institute of Technology, Pasadena, California, 91125

    Alexander B. Soshnikov

  2. Department of Mathematics, University of California, Davis, Davis, California, 95616

    Alexander B. Soshnikov

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  1. Alexander B. Soshnikov
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Soshnikov, A.B. Gaussian Fluctuation for the Number of Particles in Airy, Bessel, Sine, and Other Determinantal Random Point Fields. Journal of Statistical Physics 100, 491–522 (2000). https://doi.org/10.1023/A:1018672622921

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