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

DOI10.1209/0295-5075/100/26006arXiv1208.5669MaRDI QIDQ6235281

Publication date: 28 August 2012

Abstract: We study the directed polymer with fixed endpoints near an absorbing wall, in the continuum and in 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.

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