Communications in Mathematical Physics

, Volume 329, Issue 2, pp 641–686 | Cite as

Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

  • Florent Benaych-Georges
  • Alice Guionnet
  • Camille Male
Article

Abstract

We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Florent Benaych-Georges
    • 1
  • Alice Guionnet
    • 2
    • 3
  • Camille Male
    • 1
  1. 1.MAP 5, UMR CNRS 8145Université Paris DescartesParis Cedex 6France
  2. 2.CNRS and École Normale Supéerieure de LyonUnité de mathématiques pures et appliquéesLyon Cedex 07France
  3. 3.Mathematics DepartmentMITCambridgeUSA

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