论文标题
社区调制的递归树木和人口依赖的分支过程
Community modulated recursive trees and population dependent branching processes
论文作者
论文摘要
我们考虑通过社区调制方案生长的随机递归树，涉及随机依恋或基于学位的依恋。本文的目的是基于连续的时间嵌入以研究此类模型的一般技术。相关的连续时间嵌入不是分支过程：每次的个体生殖率取决于当时整个人群的组成。使用随机分析技术，我们表明，连续嵌入时间稳定的各种关键宏观统计量可以得出许多原始模型的功能的渐近学。
We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this paper 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 depend on the composition of the entire population at that time. 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.
