Random cutout sets with spatially inhomogeneous intensities
Tuomo Ojala, Ville Suomala, Meng Wu
TL;DR
This paper investigates the Hausdorff dimension of Poissonian cutout sets with spatially varying intensities on Ahlfors-regular metric spaces, providing formulas for self-similar and self-conformal cases using multifractal analysis.
Contribution
It introduces formulas for the Hausdorff dimension of inhomogeneous Poissonian cutout sets on Ahlfors-regular spaces, extending previous homogeneous results.
Findings
Derived formulas for Hausdorff dimension in self-similar spaces
Extended analysis to self-conformal spaces
Utilized multifractal decomposition of natural measures
Abstract
We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal spaces using the multifractal decomposition of the average densities for the natural measures.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · Advanced Mathematical Modeling in Engineering