有限随机图上的随机游动和传染病模型  

Random Walks and Epidemic Models on Finite Random Graphs

作　　者：单治超[1] 

机构地区：[1]北京大学附属中学,北京100190

出　　处：《数学进展》2017年第1期1-12,共12页Advances in Mathematics（China）

摘　　要：随机图是概率论研究的重要领域.在一个由若干图组成的集合上赋以一个概率测度,就得到一个随机图模型.关于随机图的研究主要集中于图的几何量,如最大连通分支的顶点个数、连通度、典型距离、直径、色数等,随机图模型有时也与概率论关注的其他主题进行综合,例如随机图上的随机游动和传染病模型.本文对于随机图上的随机游动和传染病模型的已有结果进行综述.Random graph is an important research field in probability theory. If we attach a probability measure on a set of graphs, we get a random graph model. Research on random graph is mainly focused on geometry of graphs, like number of vertices in the giant component, connectivity, typical distance, diameter, chromatic number, etc. Sometimes random graph model may be connected with other research topics in probability theory, like random walks and epidemic models on random graphs. In this paper we make a survey on existing results on random walks and epidemic models on random graphs.

关 键 词：有限图 随机图 随机游动 传染病模型 

分 类 号：O157.5[理学—数学] O211.62[理学—基础数学]