Directed polymer near a hard wall and KPZ equation in the half-space

We study the directed polymer with fixed endpoints near an absorbing wall, in the continuum and in the presence of disorder, equivalent to the KPZ equation on the half-space with droplet initial conditions. From a Bethe Ansatz solution of the equivalent attractive boson model we obtain the exact expression for the free-energy distribution at all times. It converges at large time to the Tracy-Widom distribution F-4 of the Gaussian symplectic ensemble (GSE). We compare our results with numerical simulations of the lattice directed polymer, both at zero and high temperature. Copyright (C) EPLA, 2012