| Issue |
Europhys. Lett.
Volume 73, Number 6, March 2006
|
|
|---|---|---|
| Page(s) | 813 - 819 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i2005-10487-1 | |
| Published online | 15 February 2006 | |
Numerical indications of a 
-generalised central limit theorem
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:
30
January
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.
PACS: 02.50.Cw – Probability theory / 02.70.Rr – General statistical methods / 05.10.-a – Computational methods in statistical physics and nonlinear dynamics
© EDP Sciences, 2006
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