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Random cutout sets with spatially inhomogeneous intensities

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyväskylä, P.O.Box 35 (MaD), 40014, Jyväskylä, Finland

    Tuomo Ojala

  2. Department of Mathematical Sciences, University of Oulu, Oulu, FI-90014, Finland

    Ville Suomala & Meng Wu

Authors
  1. Tuomo Ojala
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  2. Ville Suomala
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  3. Meng Wu
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Corresponding author

Correspondence to Ville Suomala.

Additional information

V. S. and M. W. acknowledge financial support from the Academy of Finland.

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Ojala, T., Suomala, V. & Wu, M. Random cutout sets with spatially inhomogeneous intensities. Isr. J. Math. 220, 899–925 (2017). https://doi.org/10.1007/s11856-017-1524-9

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  • DOI: https://doi.org/10.1007/s11856-017-1524-9

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