Bethe ansatz derivation of the Tracy-Widom distribution for one-dimensional directed polymers

Abstract

The distribution function of the free energy fluctuations in one-dimensional\ndirected polymers with $\\delta$-correlated random potential is studied by\nmapping the replicated problem to a many body quantum boson system with\nattractive interactions. Performing the summation over the entire spectrum of\nexcited states the problem is reduced to the Fredholm determinant with the Airy\nkernel which is known to yield the Tracy-Widom distribution\n