ISSN:
1572-9613
Keywords:
determinantal random point fields
;
central limit theorem
;
random matrices
;
Airy and Bessel kernels
;
classical compact groups
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1018672622921
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