Random cutout sets with spatially inhomogeneous intensities

Ojala, Tuomo; Suomala, Ville; Wu, Meng (2017-05-08)
 
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URL:
https://doi.org/10.1007/s11856-017-1524-9

Ojala, Tuomo
Suomala, Ville
Wu, Meng
Springer Nature
08.05.2017

Ojala, T., Suomala, V. & Wu, M. Isr. J. Math. (2017) 220: 899. https://doi.org/10.1007/s11856-017-1524-9

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© Hebrew University of Jerusalem 2017. This is a post-peer-review, pre-copyedit version of an article published in Israel journal of mathematics. The final authenticated version is available online at: http://dx.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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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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