A generalization of the Lindeberg principle

Details A generalization of the Lindeberg principle A generalization of the Lindeberg principle

2005-08-26

arxiv.org/abs/math/0508519v3

Annals of Probability 2006, Vol. 34, No. 6, 2061-2076

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000575 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

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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