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math-ph2016★ 1 cited
Higher-order Airy scaling in deformed Dyck paths
Nils Haug, Adri Olde Daalhuis, Thomas Prellberg
We introduce a deformed version of Dyck paths (DDP), where additional to the steps allowed for Dyck paths, 'jumps' orthogonal to the preferred direction of the path are permitted.…
math-ph2014★ 7 cited
Uniform asymptotics of area-weighted Dyck paths
Nils Haug, Thomas Prellberg
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 pat…