2016/10/31 by Michael Wallner · 1 citation
Computer Science · Mathematics · #Bivariate analysis #Combinatorics #Discrete mathematics #Distribution (mathematics) #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Random variable #Statistics #Stochastic processes and statistical mechanics #Uniform distribution (continuous) #Zero (linguistics) #cs.DM #math.CO #math.PR #msc:05A15 #msc:05A16
paper · pdf · doi:10.1016/j.ejc.2020.103138
published as Eur. J. Comb. Journal Profile 87, Article ID 103138, 20 p. (2020) · Long version of "A half-normal distribution scheme for generating functions and the unexpected behavior of Motzkin paths" appeared in the Proceedings of 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Krakow, Poland, 4-8 July 2016, see arXiv:1605.03046. To appear in the European Journal of Combinatorics
arxiv created 2020/04/16 · openalex publication_date 2020/04/23 · arxiv updated 2020/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a general theorem on the structure of bivariate generating functions which gives sufficient conditions such that the limiting probability distribution is a half-normal distribution. If X is a normally distributed random variable with zero mean, then |X| obeys a half-normal distribution. In the second part, we apply our result to prove three natural appearances in the domain of lattice paths: the number of returns to zero, the height, and the sign changes are under zero drift distributed according to a half-normal distribution. This extends known results to a general step set. Finally, our result also gives a new proof of Banach's matchbox problem.