Near optimal bounds for weak and strong spatial mixing for the anti-ferromagnetic Potts model on trees
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912144061104128 |
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| author | Bencs, Ferenc Berrekkal, Khallil Regts, Guus |
| author_facet | Bencs, Ferenc Berrekkal, Khallil Regts, Guus |
| contents | We show that the anti-ferromagnetic Potts model on trees exhibits strong spatial mixing for a near-optimal range of parameters. Our work complements recent results of Chen, Liu, Mani, and Moitra [arXiv.2304.01954] who showed this to be true in the infinite temperature setting, corresponding to uniform proper colorings. We furthermore prove weak spatial mixing results complementing results in [arXiv.2304.01954]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_04338 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Near optimal bounds for weak and strong spatial mixing for the anti-ferromagnetic Potts model on trees Bencs, Ferenc Berrekkal, Khallil Regts, Guus Probability Discrete Mathematics Mathematical Physics Combinatorics We show that the anti-ferromagnetic Potts model on trees exhibits strong spatial mixing for a near-optimal range of parameters. Our work complements recent results of Chen, Liu, Mani, and Moitra [arXiv.2304.01954] who showed this to be true in the infinite temperature setting, corresponding to uniform proper colorings. We furthermore prove weak spatial mixing results complementing results in [arXiv.2304.01954]. |
| title | Near optimal bounds for weak and strong spatial mixing for the anti-ferromagnetic Potts model on trees |
| topic | Probability Discrete Mathematics Mathematical Physics Combinatorics |
| url | https://arxiv.org/abs/2310.04338 |