On a \(q\) -central limit theorem consistent with nonextensive statistical mechanics
type: Item
instance of: scholarly article
title: On a \(q\) -central limit theorem consistent with nonextensive statistical mechanics
zbMATH Open document ID: 1182.60011
author: C. Tsallis
author: Sabir Umarov
author: Stanly Steinberg
published in: Milan Journal of Mathematics
publication date: 2009-11-02T00:00:00Z
review text: The basic operations of the \(q\)-algebra are defined as \(x\oplus_q y=x+y+(1-q)xy\) and \(x\otimes_q y=[x^{1-q}+y^{1-q} -1]_+^{\frac{1}{1-q}}.\) The \(q\)-generalization of the classic entropy introduced in [\textit{C. Tsallis}, J. Stat. Phys. 52, No.~1--2, 479--487 (1988; Zbl 1082.82501)] given by \(S_q=\frac{1-\sum_i p_i^q}{q-1}\),with \(q\in R\) and \(S_1=S_{BG}\), reaches its maximum at the distributions named \(q\)-Gaussians. The authors prove a generalization of Central Limit Theorem for \(1\leq q<3\).
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 82C31
zbMATH DE Number: 5624129
zbMATH Keywords: \(q\)-central limit theorem
zbMATH Keywords: correlated random variables
zbMATH Keywords: nonextensive statistical mechanics
zbMATH Keywords: \(q\)-generalization of the classic entropy
zbMATH Keywords: \(q\)-Gaussians
zbMATH Keywords: generalization of Central Limit Theorem
Wikidata QID: Q29039084
reviewed by: Nasir N. Ganikhodjaev
MaRDI profile type: Publication
full work available at URL: s00032-008-0087-y
OpenAlex ID: W2059374347
DOI: 10.1007/S00032-008-0087-Y
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description: scientific article; zbMATH DE number 5624129