Central limit theorem, deformed exponentials and superstatistics

C. Vignat; A. Plastino

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arXiv · 0706.0151

Central limit theorem, deformed exponentials and superstatistics

C. Vignat·A. Plastino

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Abstract

We show that there exists a very natural, superstatistics-linked extension of the central limit theorem (CLT) to deformed exponentials (also called q-Gaussians): This generalization favorably compares with the one provided by S. Umarov and C. Tsallis [arXiv:cond-mat/0703533], since the latter requires a special "q-independence" condition on the data. On the contrary, our CLT proposal applies exactly in the usual conditions in which the classical CLT is used. Moreover, we show that, asymptotically, the q-independence condition is naturally induced by our version of the CLT.

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C. Vignat, A. Plastino. 2007-06-01. Central limit theorem, deformed exponentials and superstatistics. https://arxiv.org/abs/0706.0151

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