# Short Time Large Deviations of the KPZ Equation

@article{Lin2020ShortTL,
title={Short Time Large Deviations of the KPZ Equation},
author={Yier Lin and Li-Cheng Tsai},
journal={arXiv: Probability},
year={2020}
}
• Published 22 September 2020
• Mathematics
• arXiv: Probability
We establish the Freidlin--Wentzell Large Deviation Principle (LDP) for the Stochastic Heat Equation with multiplicative noise in one spatial dimension. That is, we introduce a small parameter $\sqrt{\varepsilon}$ to the noise, and establish an LDP for the trajectory of the solution. Such a Freidlin--Wentzell LDP gives the short-time, one-point LDP for the KPZ equation in terms of a variational problem. Analyzing this variational problem under the narrow wedge initial data, we prove a…
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