Skip to Main content Skip to Navigation
Journal articles

Asymptotic independence in the spectrum of the Gaussian unitary ensemble

Abstract : Consider a n × n matrix from the Gaussian Unitary Ensemble (GUE). Given a finite collection of bounded disjoint real Borel sets (∆i,n, 1 ≤ i ≤ p), properly rescaled, and eventually included in any neighbourhood of the support of Wigner's semi-circle law, we prove that the related counting measures (Nn(∆i,n), 1 ≤ i ≤ p), where Nn(∆) represents the number of eigenvalues within ∆, are asymptotically independent as the size n goes to infinity, p being fixed. As a consequence, we prove that the largest and smallest eigenvalues, properly centered and rescaled, are asymptotically independent ; we finally describe the fluctuations of the condition number of a matrix from the GUE.
Document type :
Journal articles
Complete list of metadata

Cited literature [9 references]  Display  Hide  Download
Contributor : Samir Medina Perlaza Connect in order to contact the contributor
Submitted on : Saturday, January 15, 2011 - 2:16:59 PM
Last modification on : Monday, December 14, 2020 - 12:38:05 PM
Long-term archiving on: : Tuesday, November 6, 2012 - 11:35:54 AM


Files produced by the author(s)


  • HAL Id : hal-00556126, version 1



Pascal Bianchi, Merouane Debbah, Jamal Najim. Asymptotic independence in the spectrum of the Gaussian unitary ensemble. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2010, 15 (Paper 35), pp.376-395. ⟨hal-00556126⟩



Les métriques sont temporairement indisponibles