WIAS Preprint No. 3057, (2023)

Poisson approximation of fixed-degree nodes in weighted random connection models


  • Hirsch, Christian
  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Jhawar, Sanjoy Kumar
    ORCID: 0000-0003-1297-0525
  • Juhász, Péter

2020 Mathematics Subject Classification

  • 60D05 60G70 60G55 05C80


  • Poisson approximation, scale-free network, inhomogeneous random connection model, weighted random connection model, connectivity




We present a process-level Poisson-approximation result for the degree-$k$ vertices in a high-density weighted random connection model with preferential-attachment kernel in the unit volume. Our main focus lies on the impact of the left tails of the weight distribution for which we establish general criteria based on their small-weight quantiles. To illustrate that our conditions are broadly applicable, we verify them for weight distributions with polynomial and stretched exponential left tails. The proofs rest on truncation arguments and a recently established quantitative Poisson approximation result for functionals of Poisson point processes.

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