论文标题
加权递归树高的高度，具有亚物种状态增长的总重量
Height of weighted recursive trees with sub-polynomially growing total weight
论文作者
论文摘要
加权递归树是通过在树上添加带有预定权重的依次的顶点来构建的：每个新顶点都附着在随机选择的父母上，其概率与其重量成正比。如果树在步骤$ n $中的总重量以$ n $为单位增长，我们在（痛苦 - 尼兹格鲁斯2022年）中获得了树木高度的渐近扩张，该膨胀属于分支随机步行的最大分支。在本文中，我们考虑了总重量在$ n $中的总重量下生长的情况，并在几个制度中获得树高度的渐近学，表明普遍性已损坏并表现出新的行为。
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen at random with probability proportional to its weight. In the case where the total weight of the tree at step $n$ grows polynomially in $n$, we obtained in (Pain-Sénizergues 2022) an asymptotic expansion for the height of the tree, which falls into the university class of the maximum of branching random walks. In this paper, we consider the case of a total weight growing sub-polynomially in $n$ and obtain asymptotics for the height of the tree in several regimes, showing that universality is broken and exhibiting new behaviors.
