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November 2006 A generalization of the Lindeberg principle
Sourav Chatterjee
Ann. Probab. 34(6): 2061-2076 (November 2006). DOI: 10.1214/009117906000000575


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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Sourav Chatterjee. "A generalization of the Lindeberg principle." Ann. Probab. 34 (6) 2061 - 2076, November 2006.


Published: November 2006
First available in Project Euclid: 13 February 2007

zbMATH: 1117.60034
MathSciNet: MR2294976
Digital Object Identifier: 10.1214/009117906000000575

Primary: 60F17
Secondary: 15A52 , 60G09

Keywords: de Finetti , Exchangeable , invariance principle , Lindeberg , random matrices , semicircle law , Wigner

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 6 • November 2006
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