Fluctuation exponents of the half-space KPZ at stationarity

Yu Gu, Ran Tao

Published 2024-10-02Version 1

We study the half-space KPZ equation with a Neumann boundary condition, starting from stationary Brownian initial data. We derive a variance identity that links the fluctuations of the height function to the transversal fluctuations of a half-space polymer model. Utilizing this identity, we establish optimal fluctuation exponents for the height function in both the subcritical and critical regimes, along with corresponding estimates for the polymer endpoint. Additionally, we explicitly compute the average growth rate as a function of the boundary parameter.