Numerical indications of a q-generalised central limit theorem

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 - qe) beta(N)x2]1/(1 - qe), with qe = 2 - [(1)/(q)], and with coefficients beta(N) approaching finite values beta({infinity}). The particular case q = qe = 1 recovers the celebrated de Moivre-Laplace theorem.