Numerical indications of a -generalised central limit theoremL. G. Moyano1, 2, C. Tsallis1, 2 and M. Gell-Mann2
1 Centro Brasileiro de Pesquisas Físicas - Rua Xavier Sigaud 150 22290-180 Rio de Janeiro-RJ, Brazil
2 Santa Fe Institute - 1399 Hyde Park Road, Santa Fe, NM 87501, USA
received 9 September 2005; accepted in final form 30 January 2006
published online 15 February 2006
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 . We show that, in the large-N limit (and after appropriate centering, rescaling, and symmetrisation), the emerging distributions are qe-Gaussians, i.e., , with , and with coefficients approaching finite values . The particular case q=qe=1 recovers the celebrated de Moivre-Laplace theorem.
02.50.Cw - Probability theory.
02.70.Rr - General statistical methods.
05.10.-a - Computational methods in statistical physics and nonlinear dynamics.
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