特征值,不等式和遍历定理(英文)  

Eigenvalues, Inequalities and Ergodic Theory (Ⅱ)

作　　者：陈木法[1] 

机构地区：[1]北京师范大学数学系

出　　处：《数学进展》1999年第6期481-505,共25页Advances in Mathematics（China）

摘　　要：在前一文（陈（1999e））中，已综述了1992－1999年间所取得的关于标题所示的三个方面的主要成果．本文介绍用于证明这些结果的主要方法．主要有两种．其一是概率方法－耦合方法，其二是来自黎曼几何的Cheeger方法．最后，展示了遍历理论的一个新图象．本文相当自给自足．我们选择若干典型结果，给出完整的证明，并采用尽可能初等的语言．希望能为读者较快地提供这个活跃领域的新发展、新想法的概览．因论题很宽及篇幅所限，许多优美结果和大量文献均被省略．本文的部分材料已发表于陈（1994，1997，1998a）The previous paper (Chen (1999e)) surveys the main results obtained during 1992-1999 on three aspects mentioned in the title. The present paper explains the main methods used in the proofs of the mentioned results. Mainly, there are two methods. One is a probabilistic methodcoupling method; the other one is the Cheeger's method which comes from Riemannian geometry.Finally, a new picture of the ergodic theory is exhibited. This paper is rather self-contained. We choose some typical results with complete proofs and adopt the language as elementary as possible.The aim is to give the new comers a quick overview of the new progress and new ideas so that the readers may be easier to get into this active research field. Because the topics are quite wider, it is regretted that many beautiful results and a lot of references are missed, due to the limitation of the length of the paper. Parts of the materials given below has appeared in Chen (1994, 1997, 1998a).

关 键 词：特征值 不等式 遍历理论 遍历定理 马氏过程 

分 类 号：O177.99[理学—数学] O178[理学—基础数学]