分支子ordinators的最左粒子
The leftmost particle of branching subordinators
AI总结：
研究了分支子ordinators最左粒子的渐进行为，发现其位置增长速率呈亚线性，与常规分支随机游走的线性增长不同。
摘要：
我们定义了一类在非负实线上连续时间的分支粒子系统，称为分支子ordinators，其中粒子以独立的子ordinators运动。每个粒子也可以分裂（可能以无限速率）成多个子（可能无限多个），其位置相对于父粒子的位置是随机的。这些粒子系统与Bertoin和Mallein在2019年引入的分支莱维过程连续。我们特别关注分支子ordinators最左粒子的渐进行为。结果表明，在某些假设下，最左粒子位置的增长速率是t^γ，其中γ∈(0,1)取决于参数。这种亚线性增长与常规具有非负位移的分支随机游走中观察到的线性增长显著不同。
英文摘要：
We define a family of continuous-time branching particle systems on the non-negative real line, called branching subordinators, where particles move as independent subordinators. Each particle can also split (at possibly infinite rate) into several children (possibly infinitely many) whose positions relative to the position of the parent are random. These particle systems are in the continuity of branching Lévy processes introduced by Bertoin and Mallein [Ann. Probab. 47(3): 1619-1652 (2019)]. We pay a particular attention to the asymptotic behavior of the leftmost particle of branching subordinators. It turns out that, under some assumptions, the rate of growth of the position of the leftmost particle is of order $t^γ$ where $γ\in (0,1)$ depends explicitly on the parameters. This sub-linear growth is significantly different from the classical linear growth observed for regular branching random walks with non-negative displacements.
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