On the expansion of the giant component in percolated (n,d,λ) graphs

超立方体中渗流巨连通分量的直径与混合时间

Diameter and mixing time of the giant component in the percolated hypercube

研究超立方体渗流中巨连通分量的直径和混合时间，证明其规模与维度相关，并解决长期开放问题。

渗透随机几何图中第一大和第二大连通分量

On the first and second largest components in the percolated Random Geometric Graph

本文研究渗透随机几何图，证明当泊松强度超过临界值时第二大连通分量大小为 $(\log n)^2$ 阶，并证明最大连通分量经 $n$ 归一化后几乎必然收敛到常数，同时给出渗流阈值的对偶结果与收敛性。

不规则高维乘积图上的渗流

Percolation on Irregular High-dimensional Product Graphs

该研究针对高维乘积图的边渗流问题，强化了超临界区巨分支唯一性等结论，解答了基图有界度必要性、等周要求可超指数小两个问题，并发现亚临界区不规则乘积图存在多项式大分支的特殊现象。

Expansion in Supercritical Random Subgraphs of Expanders and its Consequences

In 2004, Frieze, Krivelevich and Martin [17] established the emergence of a giant component in random subgraphs of pseudo-random graphs. We study several typical properties of the giant component, most notably its expansion characteristics. We establish an asymptotic vertex expansion of connected sets in the giant by a factor of $\tilde{O}\left(ε^2\right)$. From these expansion properties, we derive that the diameter of the giant is typically $O_ε\left(\log n\right)$, and that the mixing time of a lazy random walk on the giant is asymptotically $O_ε\left(\log^2 n\right)$. We also show similar …

超临界站点渗流在正则图上的研究

Supercritical Site Percolation on Regular Graphs

研究在超临界条件下，正则图中站点渗流出现大规模连通分量的条件，揭示了超立方体和伪随机图中的新现象。

渗流超立方图中独立集的高斯到对数正态转变

Gaussian to log-normal transition for independent sets in a percolated hypercube

该研究针对超立方图键渗流子图上的硬核模型配分函数，结合概率框架与团簇展开，证明其涨落在p>2/3时呈高斯分布、p=2/3时呈双对数正态和分布，揭示了独立集的相变几何特征。