A generalization of the Lindeberg principle
Sourav Chatterjee
Source: Ann. Probab. Volume 34, Number 6
(2006), 2061-2076.
Abstract
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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Keywords: Lindeberg; de Finetti; Wigner; exchangeable; random matrices; invariance principle; semicircle law
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1171377437
Digital Object Identifier: doi:10.1214/009117906000000575
Mathematical Reviews number (MathSciNet): MR2294976
Zentralblatt MATH identifier: 1117.60034
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