Open Access
Translator Disclaimer
2020 Extensive condensation in a model of preferential attachment with fitness
Nic Freeman, Jonathan Jordan
Electron. J. Probab. 25: 1-42 (2020). DOI: 10.1214/20-EJP462


We introduce a new model of preferential attachment with fitness, and establish a time reversed duality between the model and a system of branching-coalescing particles. Using this duality, we give a clear and concise explanation for the condensation phenomenon, in which unusually fit vertices may obtain abnormally high degree: it arises from a growth-extinction dichotomy within the branching part of the dual.

We show further that the condensation is extensive. As the graph grows, unusually fit vertices become, each only for a limited time, neighbouring to a non-vanishing proportion of the current graph.


Download Citation

Nic Freeman. Jonathan Jordan. "Extensive condensation in a model of preferential attachment with fitness." Electron. J. Probab. 25 1 - 42, 2020.


Received: 18 December 2018; Accepted: 3 May 2020; Published: 2020
First available in Project Euclid: 24 June 2020

zbMATH: 1444.05131
MathSciNet: MR4115737
Digital Object Identifier: 10.1214/20-EJP462

Primary: 05C80, 60J85


Vol.25 • 2020
Back to Top