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Random fractals. (English) Zbl 0623.60020

Symmetric Cantor sets, von Koch curves and many other self-similar fractals can be considered as unique invariant sets for finite sequences of contracting similarity maps, and the Hausdorff dimension of these fractals can be computed from the contraction ratios of these similarities [see J. E. Hutchinson, Indiana Univ. Math. J. 30, 713- 747 (1981; Zbl 0598.28011)].
In this paper the author develops a corresponding theory for random self- similar fractals. The method involves an interesting treatment of flows in random networks. Independently, R. D. Mauldin and S. C. Williams, Trans. Am. Math. Soc. 295, 325-346 (1986) and S. Graf, Probab. Theory Relat. Fields 74, 357-392 (1987; Zbl 0591.60005) have obtained similar results for self-similar random fractals.
Reviewer: P.Mattila

MSC:

60D05 Geometric probability and stochastic geometry
28A75 Length, area, volume, other geometric measure theory
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References:

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