权重有界的深度加权树的深度分布
Depth profile of depth-weighted trees with bounded weights
AI总结：
研究权重有界的深度加权随机递归树，通过定义鞅结合Edgeworth展开，在权重满足大数定律时确定树深度分布的缩放极限，推广相关结果并否定一个未决问题。
摘要：
我们研究了Leckey、Mitsche和Wormald引入的深度加权随机递归树在权重上下有界的情况。当权重满足大数定律时，我们建立了这些树的深度分布的缩放极限。特别地，我们得到了这些树深度的缩放极限，推广了Lichev、Linker、Lodewijks和Mitsche的一些结果。我们还对同一作者留下的一个未决问题给出了否定答案，表明深度的缩放极限一般不成立。我们的主要工具是适当定义的鞅，结合Kabluchko、Marynych和Sulzbach引入的关于分布的一般Edgeworth展开。
英文摘要：
We study the depth-weighted random recursive trees introduced by Leckey, Mitsche and Wormald in the case where the weights are bounded from above and from below. We establish the scaling limit of the depth profile of these trees when the weights satisfy a law of large numbers. In particular, we obtain the scaling limit of the depth of these trees, generalising some results of Lichev, Linker, Lodewijks and Mitsche. We also answer negatively a question left open by the same authors, showing that the scaling limit of the depth does not hold in general. Our main tools are appropriately defined martingales combined with the general Edgeworth expansion for the profiles introduced by Kabluchko, Marynych and Sulzbach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
