Self-similar fragmentations derived from the stable tree II: splitting at nodes
Self-similar fragmentations derived from the stable tree II: splitting at nodes
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稳定树的自相似碎片二：节点分裂
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
G. Miermont
中科院分区：
文献类型：
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作者：
G. Miermont
摘要：我们研究了Duqune和Le Gall提出的一种所谓稳定树的自然碎片化过程，即按照一定的过程去除树上的节点，使碎片化具有正指数自相似性。给出了半群的显式公式，并给出了渐近结果。我们还给出了这种碎裂的另一种构造，使用L过程的路径，从而呼应了标准加法合并的两种可选构造，分别是由于Aldous-Pitman和Bertoin的分段布朗连续统随机树或使用布朗路径。
Abstract.We study a natural fragmentation process of the so-called stable tree introduced by Duquesne and Le Gall, which consists in removing the nodes of the tree according to a certain procedure that makes the fragmentation self-similar with positive index. Explicit formulas for the semigroup are given, and we provide asymptotic results. We also give an alternative construction of this fragmentation, using paths of Lévy processes, hence echoing the two alternative constructions of the standard additive coalescent by fragmenting the Brownian continuum random tree or using Brownian paths, respectively due to Aldous-Pitman and Bertoin.