Numerical indications of a q-generalised central limit theorem

LUIS G. MOYANO; CONSTANTINO TSALLIS; M. GELL-MANN

EUROPHYSICS LETTERS

EPL ASSOCIATION

Lugar: Les Ulis; Año: 2006 vol. 73 p. 813 - 819

0295-5075

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 leq 1. We show that, in the large-N limit (and after appropriate centering, rescaling, and symmetrisation), the emerging distributions are q_e-Gaussians, where q_e = 2− 1 / q , and with coefficients beta(N) approaching finite values eta(infty). The particular case q = q_e = 1 recovers the celebrated de Moivre-Laplace theorem.