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On the size of the algebraic difference of two random Cantor sets
Author(s) -
Dekking Michel,
Simon Károly
Publication year - 2008
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20178
Subject(s) - mathematics , cantor set , hausdorff dimension , cantor function , mandelbrot set , effective dimension , dimension (graph theory) , percolation (cognitive psychology) , algebraic number , set (abstract data type) , discrete mathematics , combinatorics , fractal , mathematical analysis , computer science , neuroscience , biology , programming language
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. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008