Fragmentation Processes with an Initial Mass Converging to Infinity
Fragmentation Processes with an Initial Mass Converging to Infinity
复制标题
初始质量收敛到无穷大的破碎过程
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Bénédicte Haas
中科院分区：
文献类型：
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作者：
Bénédicte Haas
摘要
我们考虑一系列破碎过程，其中粒子分裂的速率与其质量的函数成正比。令 F1(m)(t),F2(m)(t),… 表示在这样的过程中，从初始质量 m 开始，在时间 t 处出现的质量的递减重排。令m→∞。在关于碎片动力学的规则变化类型的假设下，我们证明序列（F2（m），F3（m），…）相对于Skorohod拓扑在分布上收敛于具有移民过程的碎片。这与 m−F1(m) 收敛到稳定的从属关系共同成立。还给出了与该结果相对应的连续统随机树：描述满足所需假设的自相似碎片的谱系的连续统随机树，并且从收敛到无穷大的质量开始，将收敛到具有编码带有移民的碎片的脊柱的树。
Abstract
We consider a family of fragmentation processes where the rate at which a particle splits is proportional to a function of its mass. Let F1(m)(t),F2(m)(t),… denote the decreasing rearrangement of the masses present at time t in a such process, starting from an initial mass m. Let then m→∞. Under an assumption of regular variation type on the dynamics of the fragmentation, we prove that the sequence (F2(m),F3(m),…) converges in distribution, with respect to the Skorohod topology, to a fragmentation with immigration process. This holds jointly with the convergence of m−F1(m) to a stable subordinator. A continuum random tree counterpart of this result is also given: the continuum random tree describing the genealogy of a self-similar fragmentation satisfying the required assumption and starting from a mass converging to ∞ will converge to a tree with a spine coding a fragmentation with immigration.