关于覆盖时间涨落普适性的研究
概率论
2026-01-22 v4 群论
度量几何
摘要
我们考虑有界度有限顶点传递图 上的随机游走。我们给出一个刻画覆盖时间涨落的简单几何条件：适当归一化的覆盖时间收敛到标准Gumbel变量，当且仅当 ，其中 。我们证明该条件还等价于未覆盖集的去相关。论证依赖于Tessera与Tointon近期关于Gromov多项式增长群定理有限版本的突破，我们将其转化为强热核估计，以及对Aldous与Brown击中时间指数逼近的精细定量估计，后者具有独立意义。
引用
@article{arxiv.2202.02255,
title = {On the universality of fluctuations for the cover time},
author = {Nathanaël Berestycki and Jonathan Hermon and Lucas Teyssier},
journal= {arXiv preprint arXiv:2202.02255},
year = {2026}
}
备注
v4:57 pages. Version revised following reviewer's comments. In particular, the improvement of the Aldous-Brown estimates on the exponential approximation for hitting times of sets have been separated from this article and can instead be found in arXiv:2601.03864. Section 3 in particular has also been restructured