论文标题
树木的截止很少见
Cutoff on trees is rare
论文作者
论文摘要
我们研究在树上的简单随机行走，并对混合和放松时间进行估计。依靠Basu，Hermon和Peres的最新表征，我们给出了几何标准，这些标准易于验证并允许确定截止现象是否发生。我们彻底讨论了树木的家庭家庭，并展示了如何使用我们的标准来证明几类树木的临界值，包括球形对称的树，固定高度的Galton-Watson树以及一系列随机树融合到Brownian CRT。
We study the simple random walk on trees and give estimates on the mixing and relaxation time. Relying on a recent characterization by Basu, Hermon and Peres, we give geometric criteria, which are easy to verify and allow to determine whether the cutoff phenomenon occurs. We thoroughly discuss families of trees with cutoff, and show how our criteria can be used to prove the absence of cutoff for several classes of trees, including spherically symmetric trees, Galton-Watson trees of a fixed height, and sequences of random trees converging to the Brownian CRT.
