Random cutout sets with spatially inhomogeneous intensities

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 coro...

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Bibliographic Details
Published in:Israel journal of mathematics 2017-06, Vol.220 (2), p.899-925
Main Authors: Ojala, Tuomo, Suomala, Ville, Wu, Meng
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Decomposition
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Self-similarity
Theoretical
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Summary: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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-017-1524-9