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

Details On the size of the algebraic difference of two random Cantor sets On the size of the algebraic difference of two random Cantor sets

2005-12-23

arxiv.org/abs/math/0512544v2

Random Structures and Algorithms 32 (2008), 205--222

Mathematics

Probability

This replacement corrects an important omission in the proof of Theorem 1(a)

Scientific paper

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.

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