Low temperature expansion for the Euclidean $Φ^4_2$-measure

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  • Authors: Benjamin Gess, Kihoon Seong, Pavlos Tsatsoulis
  • First public date: 2024-04-22
  • arXiv: 2404.14539
  • Preprint year: 2024
  • Status: Published
  • Publication type: Journal article
  • Publication year: 2026
  • Journal: Transactions of the American Mathematical Society, (2026)
  • DOI: 10.1090/tran/9738

Abstract

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.

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BibTeX

@article{arxiv240414539,
  title = {Low temperature expansion for the Euclidean $Φ^4_2$-measure},
  author = {Benjamin Gess and Kihoon Seong and Pavlos Tsatsoulis},
  year = {2026},
  journal = {Transactions of the American Mathematical Society, (2026)},
  doi = {10.1090/tran/9738},
  eprint = {2404.14539},
  archivePrefix = {arXiv},
  primaryClass = {math.PR}
}

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