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Mathematics > Probability

arXiv:1812.06946 (math)
[Submitted on 17 Dec 2018 (v1), last revised 23 Apr 2020 (this version, v2)]

Title:Extensive Condensation in a model of Preferential Attachment with Fitnesses

Authors: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.
Comments: 43 pages, 1 figure
Subjects: Probability (math.PR)
MSC classes: 60G99 60J85
Cite as: arXiv:1812.06946 [math.PR]
  (or arXiv:1812.06946v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.06946

Submission history

From: Nic Freeman [view email]
[v1] Mon, 17 Dec 2018 18:35:19 UTC (45 KB)
[v2] Thu, 23 Apr 2020 10:15:23 UTC (71 KB)
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