Back to Search
Start Over
Fractal percolation, porosity, and dimension
- Source :
- Journal of Theoretical Probability volume 30, pages1471-1498 (2017)
- Publication Year :
- 2015
-
Abstract
- We study the porosity properties of fractal percolation sets $E\subset\mathbb{R}^d$. Among other things, for all $0<\varepsilon<\tfrac12$, we obtain dimension bounds for the set of exceptional points where the upper porosity of $E$ is less than $\tfrac12-\varepsilon$, or the lower porosity is larger than $\varepsilon$. Our method works also for inhomogeneous fractal percolation and more general random sets whose offspring distribution gives rise to a Galton-Watson process.<br />Comment: 29 pages, 8 figures
- Subjects :
- Mathematics - Probability
60J80, 28A80, 60D05
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Theoretical Probability volume 30, pages1471-1498 (2017)
- Publication Type :
- Report
- Accession number :
- edsarx.1508.05244
- Document Type :
- Working Paper