有限图上一致生成树与环擦除随机游走的比例极限
概率论
2007-05-23 v2
摘要
设 x 和 y 在图 G 中均匀选取。在一大类包含五维及以上离散环面的图上，我们找到了从 x 到 y 的环擦除随机游走长度的极限分布。此外，在这类图上我们证明了适当标准化的有限维一致生成树的比例极限是一棵布朗连续随机树。
引用
@article{arxiv.math/0410430,
title = {Scaling limits of the uniform spanning tree and loop-erased random walk on finite graphs},
author = {Yuval Peres and David Revelle},
journal= {arXiv preprint arXiv:math/0410430},
year = {2007}
}
备注
6/6/05 version is substantially reorganized, with the main proof being more clearly presented as a proof by induction and the individual lemmas are now more self-contained