$N$-point free energy distribution function in one dimensional random   directed polymers
  Explicit expression for the $N$-point free energy distribution function in one dimensional directed polymers in a random potential is derived in terms of the Bethe ansatz replica technique. The obtained result is equivalent to the one derived earlier by Prolhac and Spohn [J. Stat. Mech., 2011, P03020]. 
V. Dotsenko
cond-mat.soft math-ph math.MP