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Pré-Publication, Document De Travail Année : 2023

Only long edges can erase the subcritical annulus-crossing phase of weight-dependent random connection models

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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.
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hal-04390273 , version 1 (12-01-2024)

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Emmanuel Jacob. Only long edges can erase the subcritical annulus-crossing phase of weight-dependent random connection models. 2023. ⟨hal-04390273⟩
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