We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this article is to derive general techniques based on continuous time embedding to study such models. The associated continuous time embeddings are not branching processes: individual reproductive rates at each time t depend on the composition of the entire population at that time, and hence vertices do not reproduce independently. Using stochastic analytic techniques we show that various key macroscopic statistics of the continuous time embedding stabilize, allowing asymptotics for a host of functionals of the original models to be derived.

中文翻译：

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社区调制的递归树和种群依赖的分支过程

我们考虑通过社区调制方案生长的随机递归树，这些方案涉及随机依恋或基于度数的依恋。本文的目的是推导出基于连续时间嵌入的通用技术来研究此类模型。相关的连续时间嵌入不是分支过程：每个时间t的个体繁殖率取决于当时整个种群的组成，因此顶点不会独立繁殖。使用随机分析技术，我们表明连续时间嵌入的各种关键宏观统计稳定，允许推导出原始模型的许多泛函的渐近线。