A generalization of the Lindeberg principle

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.

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

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• On Asymptotic Properties of Large Random Matrices with Independent Entries
• A simple invariance theorem
• Noise stability of functions with low influences: invariance and optimality

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