Abstract
The Havlin-Bunde multifractal hypothesis for the probability density of a random walker is used to obtain the scaling law of thepth-order correlation function of the concentration (for percolation) and of the height (for growing surfaces) differences:c p (r)=<|Θ(x+r)−Θ(x)|p>∼r ς p in intermittent media. It is shown that near the transition to homogeneity σ p =A p In(p/p o)(whereA andp 0 are some constants). Good agreement with recent experiments and computer simulations of different authors is established.
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Communicated by G. Weiss
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Bershadskii, A. Multifractal percolation and growth in intermittent media. J Stat Phys 87, 607–611 (1997). https://doi.org/10.1007/BF02181239
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DOI: https://doi.org/10.1007/BF02181239