Berlinkov, A. & Järvenpää, E. J Theor Probab (2019) 32: 608. https://doi.org/10.1007/s10959-019-00895-z

Porosities of Mandelbrot percolation

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Organizations: 1Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel
2University ITMO, St. Petersburg, Russian Federation
3Department of Mathematical Sciences, University of Oulu, PO Box 3000, 90014 Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
Language: English
Published: Springer Nature, 2019
Publish Date: 2020-06-01
Description:

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.

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Series: Journal of theoretical probability
ISSN: 0894-9840
ISSN-E: 1572-9230
ISSN-L: 0894-9840
Volume: 32
Issue: 2
Pages: 608 - 632
DOI: 10.1007/s10959-019-00895-z