A generalization of the Lindeberg principle

  title={A generalization of the Lindeberg principle},
  author={Sourav Chatterjee},
  journal={Annals of Probability},
  • S. Chatterjee
  • Published 26 August 2005
  • Mathematics
  • Annals of Probability
We generalize Lindeberg’s proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions of exchangeable random variables. This theorem allows us to identify, for the first time, the limiting spectral distributions of Wigner matrices with exchangeable entries. 
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CONTENTSIntroductionChapter I. Distribution of the eigenvalues and eigenvectors of random matrices § 1. Polar decomposition of random matrices § 2. Symmetric and Hermitian random matrices § 3.