Renewal, Modulation and Superstatistics

Details Renewal, Modulation and Superstatistics Renewal, Modulation and Superstatistics

2005-03-14

arxiv.org/abs/cond-mat/0503335v2

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.73.046136

We consider two different proposals to generate a time series with the same non-Poisson distribution of waiting times, to which we refer to as renewal and modulation. We show that, in spite of the apparent statistical equivalence, the two time series generate different physical effects. Renewal generates aging and anomalous scaling, while modulation yields no aging and either ordinary or anomalous diffusion, according to the prescription used for its generation. We argue, in fact, that the physical realization of modulation involves critical events, responsible for scaling. In conclusion, modulation rather than ruling out the action of critical events, sets the challenge for their identification.

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