A mapping of the unit interval of all realizations of the disorder for a random multiplicative process allows us to show that (a) the flucatuations due to different realizations of the disorder are characterized by a multifractal spectrum and (b) the fluctuations in space for a given realization of the disorder do not possess properties of self-similarity. These results have relevant implications for various physical problems with a multiplicative structure.
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Pietronero et al. (1986) studied this question.
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