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Preprints, Working Papers, ... Year : 2023

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

Abstract

We present a process-level Poisson-approximation result for the degree-k vertices in a highdensity 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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Dates and versions

hal-04434459 , version 1 (06-02-2024)

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Christian Hirsch, Benedikt Jahnel, Sanjoy Kumar Jhawar, Péter Juhász. Poisson approximation of fixed-degree nodes in weighted random connection models. 2024. ⟨hal-04434459⟩
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