Fractal percolation and branching cellular automata

被引：3
|
作者：
Dekking, FM
von der Wal, P
机构：
[1] Thomas Stieltjes Inst Math, NL-2628 CD Delft, Netherlands
[2] Delft Univ Technol, NL-2628 CD Delft, Netherlands
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2001年 / 120卷 / 02期
关键词：
random fractal set; fractal percolation; multi-type branching;
D O I：
10.1007/PL00008784
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：
Branching cellular automata (BCA) are introduced as generalisations of fractal percolation by admitting neighbour dependence. We associate sequences of random sets with BCA's and study their convergence. In case of convergence we derive the Hausdorff dimension of the limit set and of its boundary. To accomplish the latter we proof that the boundary of a set generated by a BCA is again a set generated by a BCA.
引用
收藏
页码：277 / 308
页数：32
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