Log-Gamma polymer free energy fluctuations via a Fredholm determinant   identity
  We prove that under n^{1/3} scaling, the limiting distribution as n goes to infinity of the free energy of Seppalainen's log-Gamma discrete directed polymer is GUE Tracy-Widom. The main technical innovation we provide is a general identity between a class of n-fold contour integrals and a class of Fredholm determinants. Applying this identity to the integral formula proved in [Corwin-O'Connell-Seppalainen-Zygouras] for the Laplace transform of the log-Gamma polymer partition function, we arrive at a Fredholm determinant which lends itself to asymptotic analysis (and thus yields the free energy limit theorem). The Fredholm determinant was anticipated in [Borodin-Corwin] via the formalism of Macdonald processes yet its rigorous proof was so far lacking because of the nontriviality of certain decay estimates required by that approach. 
Alexei Borodin, Ivan Corwin, Daniel Remenik
math.PR math-ph math.MP