THE ALGEBRAIC DIFFERENCE OF TWO RANDOM CANTOR SETS: THE LARSSON FAMILY

被引：5
|
作者：
Dekking, Michel [1 ]
Simon, Karoly [2 ]
Szekely, Balazs [2 ]
机构：
[1] Delft Univ Technol, Delft Inst Appl Math, NL-2628 CD Delft, Netherlands
[2] Tech Univ Budapest, Inst Math, H-1529 Budapest, Hungary
来源：
ANNALS OF PROBABILITY | 2011年 / 39卷 / 02期
关键词：
Random fractals; random iterated function systems; differences of Cantor sets; Palls conjecture; multitype branching processes;
D O I：
10.1214/10-AOP558
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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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页码：549 / 586
页数：38
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