Non-coincidence of critical points for directed polymers on supercritical percolation clusters
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918175964135424 |
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| author | Cottini, Francesca Nitzschner, Maximilian |
| author_facet | Cottini, Francesca Nitzschner, Maximilian |
| contents | We consider the model of a directed polymer in a random environment defined on the infinite cluster of supercritical Bernoulli bond percolation in dimensions $d \geq 3$. For this model, it was proved in arXiv:2205.06206 that for almost every realization of the cluster, the polymer is in a strong disorder regime for any positive inverse temperature. Here, we show for almost every realization of the cluster the existence of a non-empty sub-phase of the strong disorder regime, consisting of positive inverse temperatures in which very strong disorder does not hold. This is in contrast to the recently established sharpness of the phase transition for the directed polymer on the full lattice, see arXiv:2402.02562, arXiv:2502.04113. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-coincidence of critical points for directed polymers on supercritical percolation clusters Cottini, Francesca Nitzschner, Maximilian Probability 82D60, 82B44, 60K37, 82B43, 60K35 We consider the model of a directed polymer in a random environment defined on the infinite cluster of supercritical Bernoulli bond percolation in dimensions $d \geq 3$. For this model, it was proved in arXiv:2205.06206 that for almost every realization of the cluster, the polymer is in a strong disorder regime for any positive inverse temperature. Here, we show for almost every realization of the cluster the existence of a non-empty sub-phase of the strong disorder regime, consisting of positive inverse temperatures in which very strong disorder does not hold. This is in contrast to the recently established sharpness of the phase transition for the directed polymer on the full lattice, see arXiv:2402.02562, arXiv:2502.04113. |
| title | Non-coincidence of critical points for directed polymers on supercritical percolation clusters |
| topic | Probability 82D60, 82B44, 60K37, 82B43, 60K35 |
| url | https://arxiv.org/abs/2510.24532 |