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.

Topics
Phase transitions, Physics of gases, Euclidean geometries, Algebraic number theory, Functional equations, Asymptotic analysis, Combinatorics, Complex analysis, Statistical thermodynamics, Random walks
© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
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