Sesqui-type branching processes
Sesqui-type branching processes
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DOI：
10.1016/j.spa.2017.12.007
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发表时间：
2017-06
影响因子：
1.4
通讯作者：
S. Janson;O. Riordan;L. Warnke
中科院分区：
文献类型：
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作者：
S. Janson;O. Riordan;L. Warnke
我们考虑由两种类型（L型和S型）的粒子（个体）组成的分支过程，其中只有L型的粒子有后代，证明了生存概率和粒子总数分布（尾部）的估计。这样的过程在某种意义上更接近于单型分支过程而不是多型分支过程。尽管如此，第二种类型，贫瘠的类型，使分析显着复杂化。在这里证明的结果（关于点和生存概率）是一个关键的成分，在最近的一篇论文中，由最后两位作者的有界大小Achlioptas过程的分析。
We consider branching processes consisting of particles (individuals) of two types (type L and type S) in which only particles of type L have offspring, proving estimates for the survival probability and the (tail of) the distribution of the total number of particles. Such processes are in some sense closer to single-than to multi-type branching processes. Nonetheless, the second, barren, type complicates the analysis significantly. The results proved here (about point and survival probabilities) are a key ingredient in the analysis of bounded-size Achlioptas processes in a recent paper by the last two authors.