Uniform asymptotics of area-weighted Dyck paths
  Using the generalized method of steepest descents for the case of two coalescing saddle points, we derive an asymptotic expression for the bivariate generating function of Dyck paths, weighted according to their length and their area in the limit of the area generating variable tending towards 1. The result is valid uniformly for a range of the length generating variable, including the tricritical point of the model. 
Nils Haug and Thomas Prellberg
math-ph cond-mat.stat-mech math.CO math.MP