Porosities of Mandelbrot Percolation

Artemi Berlinkov, Esa Järvenpää

Research output: Contribution to journalArticlepeer-review

Abstract

We study porosities in the Mandelbrot percolation process using a notion of porosity that is based on the construction geometry. We show that, almost surely at almost all points with respect to the natural measure, the construction-based mean porosities of the set and the natural measure exist and are equal to each other for all parameter values outside of a countable exceptional set. As a corollary, we obtain that, almost surely at almost all points, the regular lower porosities of the set and the natural measure are equal to zero, whereas the regular upper porosities reach their maximum values.

Original languageEnglish
JournalJournal of Theoretical Probability
DOIs
StateAccepted/In press - 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Mean porosity
  • Porosity
  • Random sets

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