Electronic Journal of Probability

Extensive condensation in a model of preferential attachment with fitness

Nic Freeman and Jonathan Jordan

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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.

Article information

Electron. J. Probab., Volume 25 (2020), paper no. 68, 42 pp.

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

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Digital Object Identifier

Primary: 05C80: Random graphs [See also 60B20] 60J85: Applications of branching processes [See also 92Dxx]

preferential attachment condensation fitness random graph

Creative Commons Attribution 4.0 International License.


Freeman, Nic; Jordan, Jonathan. Extensive condensation in a model of preferential attachment with fitness. Electron. J. Probab. 25 (2020), paper no. 68, 42 pp. doi:10.1214/20-EJP462. https://projecteuclid.org/euclid.ejp/1592964036

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