Numerical indications of a q-generalised central limit theorem
| dc.creator | Moyano, Luis G. | |
| dc.creator | Tsallis, Constantino | |
| dc.creator | Gell-Mann, Murray | |
| dc.date | 2005-09-09 | |
| dc.date | 2005-12-16 | |
| dc.date.accessioned | 2026-07-07T06:41:44Z | |
| dc.date.available | 2026-07-07T06:41:44Z | |
| dc.description | We provide numerical indications of the $q$-generalised central limit theorem that has been conjectured (Tsallis 2004) in nonextensive statistical mechanics. We focus on $N$ binary random variables correlated in a {\it scale-invariant} way. The correlations are introduced by imposing the Leibnitz rule on a probability set based on the so-called $q$-product with $q \le 1$. We show that, in the large $N$ limit (and after appropriate centering, rescaling, and symmetrisation), the emerging distributions are $q_e$-Gaussians, i.e., $p(x) \propto [1-(1-q_e) β(N) x^2]^{1/(1-q_e)}$, with $q_e=2-\frac{1}{q}$, and with coefficients $β(N)$ approaching finite values $β(\infty)$. The particular case $q=q_e=1$ recovers the celebrated de Moivre-Laplace theorem. | |
| dc.description | Minor improvements and corrections have been introduced in the new version. 7 pages including 4 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0509229 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0509229 | |
| dc.identifier | Europhysics Letters 73, 813-819 (2006). | |
| dc.identifier | doi:10.1209/epl/i2005-10487-1 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101779 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Numerical indications of a q-generalised central limit theorem | |
| dc.type | text |