Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

@article{BenaychGeorges2014CentralLT,
  title={Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices},
  author={F. Benaych-Georges and A. Guionnet and C. Male},
  journal={Communications in Mathematical Physics},
  year={2014},
  volume={329},
  pages={641-686}
}
  • F. Benaych-Georges, A. Guionnet, C. Male
  • Published 2014
  • Mathematics
  • Communications in Mathematical Physics
  • 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… CONTINUE READING

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