时 间：2021年12月16日（周四）10：00-11：00
地 点：腾讯会议：733 227 245
题 目：The largest component of random intersection graph
报告人：胡治水 中国科学技术大学管理学院副教授
主持人：徐方军 教授
主 办：统计学院
摘要：
In the talk，we study the size of the largest component of the random intersection graph $G(n,m,p)$ with $m=[n^r]$ in the subcritical regime, i.e., when the expected vertex degree is smaller than one. Phase transitions occur in the subcritical random intersection graphs: if $r>1$, then the largest component is a tree of order $\Theta(\log n)$ which is the same as that of the corresponding subcritical Erdos-Renyi random graph; if $r=1$, then the largest component is no longer a tree, but the largest component and the largest tree component are both of order $\Theta(\log n)$; if $0<r<1$, then the largest tree component is of order $o(\log n)$ while the largest component is of order $\Theta(np\log n)$.
报告人简介：
胡治水，中国科学技术大学管理学院副教授，从事概率论极限理论和随机图论等领域的研究，在Ann. Statist., J. Appl. Probab., Electron, J. Probab., Econometric Theory等期刊发表学术论文40多篇，主持国家自然科学基金等多项科研项目。