高维均匀生成树的 GHP 标度极限
概率论
2022-04-14 v2 组合数学
摘要
我们证明了 Brownian 连续随机树是高维图（包括 的 维环面 、超立方体 以及传递扩张图）上均匀生成树的 Gromov-Hausdorff-Prohorov 标度极限。由此推导出若干相关量的推论：这些均匀生成树上经重标度的直径、高度和简单随机游动依分布收敛到连续随机树上相应的连续类比。
引用
@article{arxiv.2112.01203,
title = {The GHP scaling limit of uniform spanning trees in high dimensions},
author = {Eleanor Archer and Asaf Nachmias and Matan Shalev},
journal= {arXiv preprint arXiv:2112.01203},
year = {2022}
}
备注
32 pages. The proof of Lemma 2.9 in the first version of this paper is incorrect and we were unable to correct it. In this second version we provide an alternative route for the proof of the main theorems