Replica Bethe ansatz derivation of the GOE Tracy-Widom distribution in   one-dimensional directed polymers with free boundary conditions
  The distribution function of the free energy fluctuations in one-dimensional directed polymers with free boundary conditions is derived by mapping the replicated problem to the N-particle quantum boson system with attractive interactions. It is shown that in the thermodynamic limit this function is described by the universal Tracy-Widom distribution of the Gaussian orthogonal ensemble. 
Victor Dotsenko
cond-mat.stat-mech math-ph math.MP