We provide explicit conditions, in terms of the transition kernel of its driving particle, for a Markov branching process to admit a scaling limit toward a self-similar growth fragmentation with negative index. We also derive a scaling limit for the genealogical embedding considered as a compact real tree.

中文翻译：

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自相似增长片段作为马尔可夫分支过程的缩放限制

我们在其驱动粒子的过渡核方面提供了明确的条件，使马尔可夫分支过程承认向具有负指数的自相似增长碎片的缩放限制。我们还推导出被视为紧凑实树的系谱嵌入的缩放限制。