Central limit theorem for anomalous scaling due to correlations

Abstract

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.

The content of this manuscript was presented at the 3rd International Conference "Next Sigma-Phi", Kolymbari - Greece, 13-18 August 2005

References in corpus (3)

• Statistical mechanics in the context of special relativity
• Renormalization Group and Probability Theory
• Occupancy of phase space, extensivity of Sq, and q-generalized central limit theorem

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