A recursive function on a tree is a function in which each leaf has a given value, and each internal node has a value equal to a function of the number of children, the values of the children, and possibly an explicitly specified random element U . The value of the root is the key quantity of interest in general. In this study, all node values and function values are in a finite set S . In this note, we describe the limit behavior when the leaf values are drawn independently from a fixed distribution on S , and the tree T _n is a random Galton‐Watson tree of size n .

中文翻译：

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条件Galton-Watson树上的递归函数

树上的递归函数是一个函数，其中每个叶子都有给定值，每个内部节点的值等于子代数，子代值以及可能明确指定的随机元素U的函数。根的值通常是重要的关键量。在这项研究中，所有节点值和函数值都在有限集合S中。在本注释中，我们描述了当叶值独立于S的固定分布绘制时的极限行为，并且树T _n是大小为n的随机Galton-Watson树。