Ergodicity of infinite volume $Φ^4_3$ at high temperature
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913984281575424 |
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| author | Duch, Paweł Hairer, Martin Yi, Jaeyun Zhao, Wenhao |
| author_facet | Duch, Paweł Hairer, Martin Yi, Jaeyun Zhao, Wenhao |
| contents | We consider the infinite volume $Φ^4_3$ dynamic and show that it is globally well-posed in a suitable weighted Besov space of distributions. At high temperatures / small coupling, we furthermore show that the difference between any two solutions driven by the same realisation of the noise converges to zero exponentially fast. This allows us to characterise the infinite-volume $Φ^4_3$ measure at high temperature as the unique invariant measure of the dynamic, and to prove that it satisfies all Osterwalder--Schrader axioms, including invariance under translations, rotations, and reflections, as well as exponential decay of correlations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodicity of infinite volume $Φ^4_3$ at high temperature Duch, Paweł Hairer, Martin Yi, Jaeyun Zhao, Wenhao Probability Mathematical Physics Analysis of PDEs 60H15, 60H17, 60L30, 81T08, 81S20 We consider the infinite volume $Φ^4_3$ dynamic and show that it is globally well-posed in a suitable weighted Besov space of distributions. At high temperatures / small coupling, we furthermore show that the difference between any two solutions driven by the same realisation of the noise converges to zero exponentially fast. This allows us to characterise the infinite-volume $Φ^4_3$ measure at high temperature as the unique invariant measure of the dynamic, and to prove that it satisfies all Osterwalder--Schrader axioms, including invariance under translations, rotations, and reflections, as well as exponential decay of correlations. |
| title | Ergodicity of infinite volume $Φ^4_3$ at high temperature |
| topic | Probability Mathematical Physics Analysis of PDEs 60H15, 60H17, 60L30, 81T08, 81S20 |
| url | https://arxiv.org/abs/2508.07776 |