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# Short time large deviations of the KPZ equation

### Mathematical Physics and Probability Seminar

Short time large deviations of the KPZ equation
Series: Mathematical Physics and Probability Seminar
Location: Online
Presenter: Yier Lin, Columbia University

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 $\sqrt{\epsilon}$ 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 quadratic law for the near-center tail and a 5/2 law for the deep lower tail. These power laws confirm existing physics predictions in the literature. We will also discuss a limit shape problem which arises from the deep lower tail conditioning. Joint work with Li-Cheng Tsai.

(https://arizona.zoom.us/j/99811812123)