A GUE Central Limit Theorem and Universality of Directed First and Last   Passage Site Percolation
  We prove a GUE central limit theorem for random variables with finite fourth moment. We apply this theorem to prove that the directed first and last passage percolation problems in thin rectangles exhibit universal fluctuations given by the Tracy-Widom law. 
Jinho Baik and Toufic M. Suidan