Universality for directed polymers in thin rectangles
  We consider the fluctuations of the free energy of positive temperature directed polymers in thin rectangles (N,N^{\alpha}), \alpha < 3/14. For general weight distributions with finite fourth moment we prove that the distribution of these fluctuations converges as N goes to infinity to the GUE Tracy-Widom distribution. 
Antonio Auffinger, Jinho Baik, Ivan Corwin
math.PR math-ph math.MP