generating functions的半正态分布方案和Motzkin路的意外行为
A half-normal distribution scheme for generating functions and the unexpected behavior of Motzkin paths
摘要：
我们提出了一个定理的扩展迈克尔Drmota和米歇尔Soria [图像和原像随机映射，1997]，可用于确定一类组合模式的极限分布。这是通过确定相关的二元生成函数的分析和代数性质来实现的。我们给充分条件意味着一个半正态极限分布，扩展已知的条件导致无论是瑞利，高斯，或卷积的最后两个分布。我们得出结论，这样一个限制分布在域中的Motzkin路径的三个自然外观。
英文摘要：
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.
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