Work

Community modulated recursive trees and population dependent branching processes

Year: 2020

Type: preprint

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 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2004.02697

Authors: Bhamidi, Shankar, Fan, Ruituo, Fraiman, Nicolas, Nobel, Andrew

Institution: University of North Carolina at Chapel Hill

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Institutes of Health, Division of Mathematical Sciences, Army Research Office

Awards: Dynamic network models: Entrance boundary and continuum scaling limits, condensation phenomena and probabilistic combinatorial optimization, G2103075710, G2290275552, Iterative testing procedures and high-dimensional scaling limits of extremal random structures, G2944537279, G3141641755, G3561834706, Statistical and Applied Mathematical Sciences Institute, G5985085362, G6471324540, G7452299184, G8962352992, G9000029065, G9000143225

OpenAlex ID: W4287817111

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