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arxiv: math/0508519 · v3 · submitted 2005-08-26 · 🧮 math.PR

A generalization of the Lindeberg principle

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keywords theoremexchangeablefunctionslindebergprinciplerandomsmoothvariables
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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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