Low temperature expansion for the Euclidean $Φ^4_2$-measure
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916218448904192 |
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| author | Gess, Benjamin Seong, Kihoon Tsatsoulis, Pavlos |
| author_facet | Gess, Benjamin Seong, Kihoon Tsatsoulis, Pavlos |
| contents | We study asymptotic expansions of the Euclidean $Φ^4_2$-measure in the low-temperature regime. In particular, this extends the asymptotic expansions of Gaussian function space integrals developed in Schilder (1966) and Ellis and Rosen (1982) to the singular setting, where the field is no longer a function, but just a distribution. As a consequence, we deduce limit theorems, specifically the law of large numbers and the central limit theorem for the $Φ^4_2$-measure in the low-temperature limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14539 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Low temperature expansion for the Euclidean $Φ^4_2$-measure Gess, Benjamin Seong, Kihoon Tsatsoulis, Pavlos Probability Mathematical Physics Analysis of PDEs We study asymptotic expansions of the Euclidean $Φ^4_2$-measure in the low-temperature regime. In particular, this extends the asymptotic expansions of Gaussian function space integrals developed in Schilder (1966) and Ellis and Rosen (1982) to the singular setting, where the field is no longer a function, but just a distribution. As a consequence, we deduce limit theorems, specifically the law of large numbers and the central limit theorem for the $Φ^4_2$-measure in the low-temperature limit. |
| title | Low temperature expansion for the Euclidean $Φ^4_2$-measure |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2404.14539 |