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

Christian Hirsch, Benedikt Jahnel, Sanjoy Kumar Jhawar and Peter Juhasz

Stochastic Processes and their Applications, 2025, vol. 183, issue C

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.

Keywords: Poisson approximation; Scale-free network; Inhomogeneous random connection model; Weighted random connection model; Connectivity (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104593

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