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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.07254 |
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| _version_ | 1866912636347613184 |
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| author | Prodromidis, Kyprianos-Iason Sly, Allan |
| author_facet | Prodromidis, Kyprianos-Iason Sly, Allan |
| contents | We consider the stochastic Ising model on sparse Erdos-Renyi graphs $G(n,d/n)$ with $d>1$ at the critical temperature $β_c=\tanh^{-1}(d^{-1})$ and prove that with high probability, the mixing time is at most polynomial in $n$. Our approach combines the recent stochastic localization framework of Chen and Eldan, which yields spectral gap bounds in the well-behaved bulk of the graph, together with classical results on the relaxation time of Glauber dynamics on trees to handle regions where we cannot apply the Chen-Eldan method directly because of atypically large local neighborhoods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07254 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial mixing of the critical Ising model on sparse Erdos-Renyi graphs Prodromidis, Kyprianos-Iason Sly, Allan Probability We consider the stochastic Ising model on sparse Erdos-Renyi graphs $G(n,d/n)$ with $d>1$ at the critical temperature $β_c=\tanh^{-1}(d^{-1})$ and prove that with high probability, the mixing time is at most polynomial in $n$. Our approach combines the recent stochastic localization framework of Chen and Eldan, which yields spectral gap bounds in the well-behaved bulk of the graph, together with classical results on the relaxation time of Glauber dynamics on trees to handle regions where we cannot apply the Chen-Eldan method directly because of atypically large local neighborhoods. |
| title | Polynomial mixing of the critical Ising model on sparse Erdos-Renyi graphs |
| topic | Probability |
| url | https://arxiv.org/abs/2510.07254 |