稀疏重尾随机交图上随机游走的外围陷阱与混合时间下界
Peripheral Traps and Lower Bounds on Mixing Times for Random Walks on Sparse Heavy-Tailed Random Intersection Graphs
中文总结 AI 辅助
本文针对稀疏重尾随机交图上的随机游走，分析其混合时间下界，发现外围陷阱导致混合时间下界为Ω(log²n)，局部总变差距离非集中衰减，进而指出不存在全局截断。
中文摘要 AI 辅助
本文分析稀疏重尾随机交图上随机游走的混合时间下界。在稀疏特征 regime 中，重尾特征分布会形成外围陷阱——即连接图巨分量内高权重枢纽节点的重叠低权重特征团链。通过将从这些陷阱的逃逸轨迹建模为反射布朗运动的连续极限击中时间，分析表明随机游走会经历对数平方延迟。因此，混合时间下界为Ω(log²n)，且局部总变差距离呈现非集中衰减。这种局部阻碍阻止了这些初始状态出现尖锐截断现象，若全局混合时间为相同对数平方阶，则有条件地意味着不存在全局截断。
英文摘要
This paper analyzes mixing time lower bounds for random walks on sparse, heavy-tailed Random Intersection Graphs. In sparse feature regimes, heavy-tailed feature distributions lead to the formation of peripheral trap -- chains of overlapping low-weight feature cliques attached to high-weight hub nodes within the graph's giant component. By modeling escape trajectories from these traps as continuous limit hitting times for reflected Brownian motion, the analysis demonstrates that random walks experience logarithmic squared delays. Consequently, the mixing time is bounded below by $Ω(\log^2 n)$, and the local total variation distance exhibits non-concentrated decay, formally preventing a sharp cutoff phenomenon.
