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

Author

Listed:
  • Hirsch, Christian
  • Jahnel, Benedikt
  • Jhawar, Sanjoy Kumar
  • Juhasz, Peter

Abstract

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 a finite-volume Borel set. 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.

Suggested Citation

  • Hirsch, Christian & Jahnel, Benedikt & Jhawar, Sanjoy Kumar & Juhasz, Peter, 2025. "Poisson approximation of fixed-degree nodes in weighted random connection models," Stochastic Processes and their Applications, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:spapps:v:183:y:2025:i:c:s0304414925000341
    DOI: 10.1016/j.spa.2025.104593
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