On the small time asymptotics of the dynamical $\Phi^4_1$ model

TL;DR

This paper derives small time large deviation principles for the dynamical _1 model, analyzing the impact of space-time white noise and small nonlinear drift on the system's behavior.

Contribution

It establishes the first small time asymptotics for the dynamical _1 model, including effects of small noise and nonlinear drift.

Findings

Large deviation principle for small time _1 model

Quantitative analysis of noise and drift effects

Framework for future small time asymptotic studies

Abstract

In this paper, we establish a small time large deviation principle (small time asymptotics) for the dynamical $\Phi^4_1$ model, which not only involves study of the space-time white noise with intensity $\sqrt{\varepsilon}$, but also the investigation of the effect of the small (with $\varepsilon$) nonlinear drift.