Low temperature expansion for the Euclidean Φ^4_2-measure
arxiv(2024)
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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