Lower tail of the KPZ equation

Abstract

We provide the first tight bounds on the lower tail probability of the one-point distribution of the Kardar–Parisi–Zhang (KPZ) equation with narrow wedge initial data. Our bounds hold for all sufficiently large times T and demonstrates a crossover between superexponential decay with exponent 52 (and leading prefactor 415πT1/3) for tail depth greater than T2/3, and exponent 3 (with leading prefactor at least 112) for tail depth less than T2/3.

Topics & Concepts