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 in
Israel Journal of MathematicsDate
2017Discipline
MatematiikkaCopyright
© 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.