Intermediate Disorder Regime for Half-Space Directed Polymers

We consider the convergence of point-to-point partition functions for the half-space directed polymer model in dimension 1+1 in the intermediate disorder regime as introduced for the full space model by Alberts, Khanin and Quastel in []. By scaling the inverse temperature as $\beta n^{-1/4}$, the point-to-point partition function converges to the chaos series for the solution to stochastic heat equation with Robin boundary condition and delta initial data. Furthermore, the convergence result is then applied to the exact-solvable log-gamma directed polymer model in a half-space.