Random cutout sets with spatially inhomogeneous intensities
Ojala, T., Suomala, V., & Wu, M. (2017). Random cutout sets with spatially inhomogeneous intensities. Israel Journal of Mathematics, 220 (2), 899-925. doi:10.1007/s11856-017-1524-9
Published inIsrael Journal of Mathematics
© Hebrew University of Jerusalem 2017. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
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.