Central limit theorem for anomalous scaling due to correlations.
We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling and is based on a correspondence with the Lévy-Gnedenko uncorrelated case. In particular, correlated anomalous diffusion is mapped onto Lévy diffusion. Under suitable assumptions, the nonstandard multiplicative structure used for constructing the characteristic function of the total sum allows us to determine correlations of partial sums exclusively on the basis of the global anomalous scaling.
Baldovin
Fulvio
F
Dipartimento di Fisica and Sezione INFN, Universitá di Padova, Via Marzolo 8, I-35131 Padova, Italy. baldovin@pd.infn.it
Stella
Attilio L
AL