I will discuss the asymptotic expansions of the Euclidean Φ^4-measure in the low-temperature regime. Consequently, we derive limit theorems, specifically the law of large numbers and the central limit theorem for the Φ^4-measure in the low-temperature limit. In the second part of the talk, I will focus on the infinite volume limit of the focusing Φ^4-measure. Specifically, with appropriate scaling, the focusing Φ^4-measure exhibits Gaussian fluctuations around a scaled solitary wave, that is, the central limit theorem.
This talk is based on joint works with Benjamin Gess, Pavlos Tsatsoulis, and Philippe Sosoe.