A generalization of the Lindeberg principle
نویسنده
چکیده
We present a generalization of Lindeberg’s method of proving the central limit theorem to encompass general smooth functions (instead of just sums) and dependent random variables. The technique is then used to obtain an invariance result for smooth functions of exchangeable random variables. As an illustrative application of this theorem, we then establish “convergence to Wigner’s law” for eigenspectra of matrices with exchangeable random entries.
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