On the size of the algebraic difference of two random cantor sets

Michel Dekking, Károly Simon

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In this paper we consider some families of random Cantor sets on the line and investigate the question whether the condition that the sum of Hausdorff dimension is larger than one implies the existence of interior points in the difference set of two independent copies. We prove that this is the case for the so called Mandelbrot percolation. On the other hand the same is not always true if we apply a slightly more general construction of random Cantor sets. We also present a complete solution for the deterministic case.

Original languageEnglish
Pages (from-to)205-222
Number of pages18
JournalRandom Structures and Algorithms
Volume32
Issue number2
DOIs
Publication statusPublished - Mar 1 2008

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Keywords

  • Difference of Cantor sets
  • Mandelbrot percolation
  • Multitype branching processes in varying environment
  • Palis conjecture
  • Random fractals
  • Superbranching processes

ASJC Scopus subject areas

  • Software
  • Mathematics(all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

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