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March 2011 The algebraic difference of two random Cantor sets: The Larsson family
Michel Dekking, Károly Simon, Balázs Székely
Ann. Probab. 39(2): 549-586 (March 2011). DOI: 10.1214/10-AOP558


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.


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Michel Dekking. Károly Simon. Balázs Székely. "The algebraic difference of two random Cantor sets: The Larsson family." Ann. Probab. 39 (2) 549 - 586, March 2011.


Published: March 2011
First available in Project Euclid: 25 February 2011

zbMATH: 1223.28011
MathSciNet: MR2789506
Digital Object Identifier: 10.1214/10-AOP558

Primary: 28A80
Secondary: 60J80 , 60J85

Keywords: differences of Cantor sets , Multitype branching processes , Palis conjecture , Random fractals , random iterated function systems

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 2 • March 2011
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