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

### Random cutout sets with spatially inhomogeneous intensities

Saved in:
Author: Ojala, Tuomo1; Suomala, Ville2; Wu, Meng2
Organizations: 1Department of Mathematics and Statistics, University of Jyväskylä P.O.Box 35 (MaD), 40014 University of Jyväskylä, Finland
2Department of Mathematical Sciences, FI-90014 University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.4 MB)
Language: English
Published: Springer Nature, 2017
Publish Date: 2018-05-08
Description:

# 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.

see all

Series: Israel journal of mathematics
ISSN: 0021-2172
ISSN-E: 1565-8511
ISSN-L: 0021-2172
Volume: 220
Issue: 2
Pages: 899 - 925
DOI: 10.1007/s11856-017-1524-9