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M. Wallner:
"A half-normal distribution scheme for generating functions and the unexpected behaviour of Motzkin paths";
Vortrag: AofA 2016 - 27th. International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis, Kraków, Polen; 04.07.2016 - 08.07.2016; in: "Proceedings of the 27 International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms", (2016), S. 341 - 352.

We present an extension of a theorem by Michael Drmota and Michèle Soria [Images and Preimages in Random Mappings, 1997] that can be used to identify the limiting distribution for a class of combinatorial schemata. This is achieved by determining analytical and algebraic properties of the associated bivariate generating function. We give sufficient conditions implying a half-normal limiting distribution, extending the known conditions leading to either a Rayleigh, a Gaussian, or a convolution of the last two distributions. We conclude with three natural appearances of such a limiting distribution in the domain of Motzkin paths.