Extensive Condensation in a model of Preferential Attachment with Fitnesses

Nic Freeman; Jonathan Jordan

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arXiv · 1812.06946

Extensive Condensation in a model of Preferential Attachment with Fitnesses

Nic Freeman·Jonathan Jordan

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Abstract

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.

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Nic Freeman, Jonathan Jordan. 2020-04-23. Extensive Condensation in a model of Preferential Attachment with Fitnesses. https://arxiv.org/abs/1812.06946

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