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Numerical indications of a q-generalised central limit theorem

Moyano, L. G. and Tsallis, C. and Gell-Mann, M. (2006) Numerical indications of a q-generalised central limit theorem. Europhysics Letters, 73 (6). pp. 813-819. ISSN 0295-5075.

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We provide numerical indications of the q-generalised central limit theorem that has been conjectured ( TSALLIS C., Milan J. Math., 73 (2005) 145) in nonextensive statistical mechanics. We focus on N binary random variables correlated in a scale-invariant way. The correlations are introduced by imposing the Leibnitz rule on a probability set based on the so-called q-product with q ≤ 1. We show that, in the large-N limit (and after appropriate centering, rescaling, and symmetrisation), the emerging distributions are qe-Gaussians, i.e., p(x) ∝ [1-(1-q_e), β(N)x^2]^{1/(1-q_e)}, with q_e=2-(1/q), and with coefficients β(N) approaching finite values β(∞). The particular case q=q_e=1 recovers the celebrated de Moivre-Laplace theorem.

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Additional Information:© 2006 EDP Sciences. Received 9 September 2005; accepted in final form 30 January 2006; published online 15 February 2006. Longstanding conversations on the subject of two of us (LGM and CT) with F. BALDOVIN, E. P. Borges and S. M. D. QUEIROS, and useful remarks from J. D. FARMER, F. LILLO, S. STEINBERG and H. SUYARI are acknowledged. We have benefitted from partial financial support by Pronex/MCT, Faperj and CNPq (Brazil), and SI International and AFRL (USA). MG-M was generously supported by the COUQ Foundation and by Insight Venture Management.
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Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ)UNSPECIFIED
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)UNSPECIFIED
Air Force Research Laboratory (AFRL)UNSPECIFIED
Insight Venture ManagementUNSPECIFIED
Issue or Number:6
Classification Code:PACS 02.50.Cw - Probability theory 02.70.Rr - General statistical methods 05.10.-a - Computational methods in statistical physics and nonlinear dynamics
Record Number:CaltechAUTHORS:20150824-124357646
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Official Citation:Numerical indications of a q-generalised central limit theorem L. G. Moyano - C. Tsallis - M. Gell-Mann Europhys. Lett., 73 (6), p. 813 (2006) DOI: 10.1209/epl/i2005-10487-1
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:59849
Deposited By: George Porter
Deposited On:24 Aug 2015 20:19
Last Modified:03 Oct 2019 08:50

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