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

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

2009-01-21

arxiv.org/abs/0901.3304v2

Annals of Probability 2011, Vol. 39, No. 2, 549-586

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOP558 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

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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