Dimension (in)equalities and Holder continuous curves in fractal percolation

M.T. Joosten, E.I. Broman, F. Camia, R.W.J. Meester

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We relate various concepts of fractal dimension of the limiting set C in fractal percolation to the dimensions of the set consisting of connected components larger than one point and its complement in C (the "dust"). In two dimensions, we also show that the set consisting of connected components larger than one point is almost surely the union of non-trivial Hölder continuous curves, all with the same exponent. Finally, we give a short proof of the fact that in two dimensions, any curve in the limiting set must have Hausdorff dimension strictly larger than 1. © 2012 The Author(s).
Original languageEnglish
Pages (from-to)836-855
Number of pages19
JournalJournal of Theoretical Probability
Volume26
Issue number3
Early online date23 Mar 2012
DOIs
Publication statusPublished - Sept 2013

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