Hodge-GUE correspondence and the discrete KdV equation
  We prove the conjectural relationship recently proposed in [9] between certain special cubic Hodge integrals of the Gopakumar--Mari\~no--Vafa type [17, 28] and GUE correlators, and the conjecture proposed in [7] that the partition function of these Hodge integrals is a tau function of the discrete KdV hierarchy. 
Boris Dubrovin, Si-Qi Liu, Di Yang, Youjin Zhang
math-ph math.AG math.MP