发表机构
Paris Dauphine University; University of British Columbia; King’s College and DPMMS, University of Cambridge; Department of Mathematics, Princeton University; University of Cambridge（巴黎第九大学; 不列颠哥伦比亚大学; 剑桥大学国王学院与应用数学与理论物理系; 普林斯顿大学数学系; 剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究三维及以上小世界网络上随机游走的混合时间，证明其阶为对数阶且无截断现象。
AI 中文摘要
我们研究在$\nmathbb{Z}_n^d$上通过如下方式添加边所定义的小世界网络上简单随机游走的混合时间：对于每一对$\n{x,y\b}$，以概率$Z_n/\n|x-y\b|^{d}$添加一条边，其中$Z_n$的选择使得每个顶点平均添加的边数为$1$。当$d\geq 3$时，我们证明以高概率混合时间的阶为$\log n$，且该随机游走不呈现截断现象。
英文摘要
We study the mixing time of a simple random walk on the small-world network defined by adding edges to $\mathbb{Z}_n^d$ as follows: for each pair $\{x,y\}$ we add an edge with probability $Z_n/\|x-y\|^{d}$ with $Z_n$ chosen so that the average number of added edges to every vertex is $1$. When $d\geq 3$, we show that with high probability the mixing time is of order~$\log n$ and that the random walk does not exhibit cutoff.
