Limit theory for isolated and extreme points in hyperbolic random geometric graphs

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Colleges, School and Institutes

External organisations

  • Lehigh University


We establish expectation and variance asymptotics as well as asymptotic normality for the number of isolated and extreme points in a model of random geometric graphs on the hyperbolic plane. We show that the limit theory and renormalization for the number of isolated points are highly sensitive on the curvature parameter.
In particular, if the parameter that tunes the curvature is between 1/2 and 1, then the variance is super-linear, when it is equal to 2 the variance is linear with a logarithmic correction, whereas when this exceeds 1 the variance is linear.
The central limit theorem fails within the first regime but holds for the last regime.


Original languageEnglish
Number of pages51
JournalElectronic Journal of Probability
Publication statusPublished - 2020


  • Hyperbolic plane, complex networks, central limit theorem, Random geometric graph

ASJC Scopus subject areas