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

1999/07/15 by Alexander B. Soshnikov, Soshnikov, Alexander B. · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.math-ph/9907012

The essential alterations are a slightly different formulation of the Costin-Lebowitz Theorem and the addition of Remark 4 in the section 2

arxiv created 1999/12/14 · arxiv updated 2009/11/30

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.

Cited by

• Universality for fluctuations of counting statistics of random normal matrices

Related

• Deviations from the Circular Law
• Partial linear eigenvalue statistics for non-Hermitian random matrices
• Fluctuations of the eigenvalue number in the fixed interval for β-models with β=1,2,4
• Gaussian fluctuations for linear spectral statistics of Wigner beta ensembles
• Universal Gaussian fluctuations of non-Hermitian matrix ensembles: from weak convergence to almost sure CLTs