Community modulated recursive trees and population dependent branching processes
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 21, 2021
- Source ID
- 10.1002/rsa.21027
Entities
People
- Andrew Nobel
- Nicolas Fraiman
- Ruituo Fan
- Shankar Bhamidi
Organizations
- Army Research Office
- National Science Foundation
- University of North Carolina