Random cutout sets with spatially inhomogeneous intensities |
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Authors: | Tuomo Ojala Ville Suomala Meng Wu |
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Institution: | 1.Department of Mathematics and Statistics,University of Jyv?skyl?,Jyv?skyl?,Finland;2.Department of Mathematical Sciences,University of Oulu,Oulu,Finland |
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Abstract: | We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Q-regular metric spaces. Our main results explain the dependence of the dimension of the cutout sets on the multifractal structure of the average densities of the Q-regular measure. As a corollary, we obtain formulas for the Hausdorff dimension of such cutout sets in self-similar and self-conformal spaces using the multifractal decomposition of the average densities for the natural measures. |
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