Central limit theorem for anomalous scaling due to correlations

Details Central limit theorem for anomalous scaling due to correlations Central limit theorem for anomalous scaling due to correlations

2005-10-10

arxiv.org/abs/cond-mat/0510225v2

Phys. Rev. E {\bf 75}, 020101(R) (2007)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

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 L\'evy-Gnedenko uncorrelated case. In particular, correlated anomalous diffusion is mapped onto L\'evy 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.

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