有限图上首达时等随机变量的极限定理  

Limit Theorems of Random Variables Like First Passage Time on Finite 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》2016年第4期481-490,共10页Advances in Mathematics（China）

摘　　要：1965年,Hammersley和Welsh在["Bernoulli 1713,Bayes 1763,Laplace 1813",1965,61-110]里提出了首达渗流模型.此后对该模型的研究主要集中于无限图,特别是整数格点Z^d上.近年来一些概率学家开始关注有限图上的首达渗流模型.有限图上首达渗流模型的关注点与无限图上有截然不同,主要涉及首达时、跳数、淹没时、直径等随机变量的极限行为.本文对于有限图上首达渗流模型的首达时等随机变量的极限定理进行了综述.In 1965 Hammersley and Welsh introduced the first passage percolation model in [＂Bernoulli 1713, Bayes 1763, Laplace 1813＂, 1965, 61-110]. Since then the research oil first passage percolation is mainly focused on infinite graph cases, especially on Zd. Recently, some probabilists begin to be concerned about finite graph cases. Interesting problems of first passage percolation models on finite graph cases, which are quite different from infinite graph cases, are mainly related to the limiting behaviors of first passage times, hopcounts, flooding times, diameters, etc. In this paper we make a survey on results about limit theorems of random variables like first passage time on finite graphs.

关 键 词：有限图 随机图 首达时 直径 随机变量 极限定理 

分 类 号：O157.5[理学—数学] O211.4[理学—基础数学]