The lower tail of the half-space KPZ equation

We establish the first tight bound on lower tail probability of half-space KPZ equation with Neumann boundary parameter A=−1/2 and narrow-wedge initial data. The demonstrates a crossover between two regimes super-exponential decay exponents 52 3; upper 32 3. Given crude leading-order asymptotic in Stokes region for Ablowitz–Segur solution to Painlevé II (Definition 1.8), we improve demonstrate same as bound. also novel bounds large deviations GOE point process.