  In this paper, we consider the KPZ equation under the weak noise scaling.
That is, we introduce a small parameter $\sqrt{\varepsilon}$ in front of the
noise and let $\varepsilon \to 0$. We prove that the one-point large deviation
rate function has a $\frac{3}{2}$ power law in the deep upper tail.
Furthermore, by forcing the value of the KPZ equation at a point to be very
large, we prove a limit shape of the KPZ equation as $\varepsilon \to 0$. This
confirms the physics prediction in Kolokolov and Korshunov (2007), Kolokolov
and Korshunov (2009), Meerson, Katzav, and Vilenkin (2016), Kamenev, Meerson,
and Sasorov (2016), and Le Doussal, Majumdar, Rosso, and Schehr (2016).
