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

TL;DR

This paper develops low-temperature asymptotic expansions for the Euclidean ^4_2-measure, extending classical Gaussian integral results to a singular distribution setting, and establishes related limit theorems.

Contribution

It introduces a novel low-temperature expansion for the ^4_2-measure, extending classical Gaussian integral asymptotics to a singular distribution framework.

Findings

Derived low-temperature asymptotic expansions for ^4_2-measure.

Proved law of large numbers in the low-temperature limit.

Established central limit theorem for the ^4_2-measure.

Abstract

We study asymptotic expansions of the Euclidean $\Phi^4_2$-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 $\Phi^4_2$-measure in the low-temperature limit.