Fluctuations of half-space KPZ: from 1/2 to 1/3

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. We then obtain estimates for the polymer endpoint, which gives us optimal fluctuation exponents for the height function in both the subcritical and critical regimes, as well as an optimal upper bound for the fluctuation exponents in the supercritical regime. Based on a joint work with Yu Gu.