Only long edges can erase the subcritical annulus-crossing phase of weight-dependent random connection models
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916513549647872 |
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| author | Jacob, Emmanuel |
| author_facet | Jacob, Emmanuel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04023 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Only long edges can erase the subcritical annulus-crossing phase of weight-dependent random connection models Jacob, Emmanuel Probability 60K35, 82B43 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. |
| title | Only long edges can erase the subcritical annulus-crossing phase of weight-dependent random connection models |
| topic | Probability 60K35, 82B43 |
| url | https://arxiv.org/abs/2311.04023 |