The algebraic difference of two random Cantor sets: The Larsson family

Michel Dekking, Károly Simon, Balázs Székely

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we consider a family of random Cantor sets on the line and consider the question of whether the condition that the sum of the Hausdorff dimensions is larger than one implies the existence of interior points in the difference set of two independent copies. We give a new and complete proof that this is the case for the random Cantor sets introduced by Per Larsson.

Original languageEnglish
Pages (from-to)549-586
Number of pages38
JournalAnnals of Probability
Volume39
Issue number2
DOIs
Publication statusPublished - Mar 1 2011

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Keywords

  • Differences of Cantor sets
  • Multitype branching processes
  • Palis conjecture
  • Random fractals
  • Random iterated function systems

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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