Only long edges can erase the subcritical annulus-crossing phase of weight-dependent random connection models
Résumé
This short note aims at complementing the results of the recent work arXiv:2302.05396, where Jahnel and Lüchtrath investigate the question of existence of a subcritical percolation phase for the annulus-crossing probabilities in a large class of continuum percolation models, namely the classical or generalized weight-dependent random connection models. Their work relates the absence of a subcritical phase to the occurrence of long edges in the graph, through a somewhat indirect criterium, that stays inconclusive in some models of interest. We provide a more direct and arguably simpler criterium, that is always conclusive when considering classical weight-dependent random connection models.
Domaines
Probabilités [math.PR]
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Existence_of_subcritical_phase_dichotomy_arxiv.pdf (128.15 Ko)
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