Loop percolation versus link percolation in the random loop model
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915498301587456 |
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| author | Betz, Volker Klippel, Andreas Kraft, Mino Nicola |
| author_facet | Betz, Volker Klippel, Andreas Kraft, Mino Nicola |
| contents | In [Muhl2019], Peter Mühlbacher showed that in the random loop model without loop weights, a loop phase transition (assuming it exists) cannot occur at the same parameter as the percolation phase transition of the occupied edges. In this work, we give a quantitative version of this result, specifying a minimal gap between the percolation phase transition and a possible loop phase transition. A substantial part of our argument also works for weighted loop models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Loop percolation versus link percolation in the random loop model Betz, Volker Klippel, Andreas Kraft, Mino Nicola Probability In [Muhl2019], Peter Mühlbacher showed that in the random loop model without loop weights, a loop phase transition (assuming it exists) cannot occur at the same parameter as the percolation phase transition of the occupied edges. In this work, we give a quantitative version of this result, specifying a minimal gap between the percolation phase transition and a possible loop phase transition. A substantial part of our argument also works for weighted loop models. |
| title | Loop percolation versus link percolation in the random loop model |
| topic | Probability |
| url | https://arxiv.org/abs/2408.00648 |