论文标题
随机图的刚性的尖锐阈值
Sharp threshold for rigidity of random graphs
论文作者
论文摘要
我们考虑随机图的ERDőS-rényi演变，其中在每个步骤中都添加了新的均匀分布的边缘。对于每一个固定的$ d \ ge 1 $，我们都表明，概率很高，该图在$ \ mathbb r^d $的那一刻就变为刚性，其最低度变为$ d $，并且它在$ \ mathbb r^d $中在全球上变得僵化，而其最低度为$ d+1 $。
We consider the Erdős-Rényi evolution of random graphs, where a new uniformly distributed edge is added to the graph in every step. For every fixed $d\ge 1$, we show that with high probability, the graph becomes rigid in $\mathbb R^d$ at the very moment its minimum degree becomes $d$, and it becomes globally rigid in $\mathbb R^d$ at the very moment its minimum degree becomes $d+1$.
