Soshnikov, Alexander B. Gaussian fluctuation for the number of particles in Airy, Bessel, sine, and other determinantal random point fields. (English) Zbl 1041.82001 J. Stat. Phys. 100, No. 3-4, 491-522 (2000). Summary: 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. Cited in 1 ReviewCited in 39 Documents MSC: 82B05 Classical equilibrium statistical mechanics (general) 60F99 Limit theorems in probability theory 82B31 Stochastic methods applied to problems in equilibrium statistical mechanics 15B52 Random matrices (algebraic aspects) Keywords:determinantal random point fields; central limit theorem; random matrices; Airy kernel; Bessel kernel; classical compact groups PDF BibTeX XML Cite \textit{A. B. Soshnikov}, J. Stat. Phys. 100, No. 3--4, 491--522 (2000; Zbl 1041.82001) Full Text: DOI arXiv OpenURL