Random point fields with Markovian refinements and the geometry of fractally disordered media |
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Authors: | Yu P Virchenko O L Shpilinskaya |
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Institution: | (1) Institute for Monocrystals, National Academy of Sciences of the Ukraine, Kharkov, The Ukraine |
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Abstract: | We give a general construction of the probability measure for describing stochastic fractals that model fractally disordered
media. For these stochastic fractals, we introduce the notion of a metrically homogeneous fractal Hansdorff-Karathéodory measure
of a nonrandom type. We select a classFq] of random point fields with Markovian refinements for which we explicitly construct the probability distribution. We prove
that under rather weak conditions, the fractal dimension D for random fields of this class is a self-averaging quantity and
a fractal measure of a nonrandom type (the Hausdorff D-measure) can be defined on these fractals with probability 1.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 3, pp. 490–505, September, 2000. |
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