Local criteria for global connectivity comparisons: beyond stochastic domination
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866917354458316800 |
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| author | Bäumler, Johannes Jahnel, Benedikt Köppl, Jonas Lodewijks, Bas Reeves, Lily Tóbiás, András |
| author_facet | Bäumler, Johannes Jahnel, Benedikt Köppl, Jonas Lodewijks, Bas Reeves, Lily Tóbiás, András |
| contents | We introduce a site-wise domination criterion for local percolation models, which enables the comparison of one-arm probabilities even in the absence of stochastic domination. The method relies on a local-to-global principle: if, at each site, one model is more likely than the other to connect to a subset of its neighbors, for all nontrivial such subsets, then this advantage propagates to connectivity events at all scales. In this way, we obtain a robust alternative to stochastic domination, applicable in all cases where the latter works and in many where it does not. As a main application, we compare classical Bernoulli bond percolation with degree-constrained models, showing that degree constraints enhance percolation, and obtain asymptotically optimal bounds on critical parameters for degree-constrained models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03934 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local criteria for global connectivity comparisons: beyond stochastic domination Bäumler, Johannes Jahnel, Benedikt Köppl, Jonas Lodewijks, Bas Reeves, Lily Tóbiás, András Probability primary 60K35, secondary 82B43 We introduce a site-wise domination criterion for local percolation models, which enables the comparison of one-arm probabilities even in the absence of stochastic domination. The method relies on a local-to-global principle: if, at each site, one model is more likely than the other to connect to a subset of its neighbors, for all nontrivial such subsets, then this advantage propagates to connectivity events at all scales. In this way, we obtain a robust alternative to stochastic domination, applicable in all cases where the latter works and in many where it does not. As a main application, we compare classical Bernoulli bond percolation with degree-constrained models, showing that degree constraints enhance percolation, and obtain asymptotically optimal bounds on critical parameters for degree-constrained models. |
| title | Local criteria for global connectivity comparisons: beyond stochastic domination |
| topic | Probability primary 60K35, secondary 82B43 |
| url | https://arxiv.org/abs/2510.03934 |