作者：陈木法
页数：228
出版社：世界图书出版公司
出版日期：2013
ISBN：9787510052675
电子书格式：pdf/epub/txt
内容简介
this book surveys， in a popular way， the main progress made in
the field by our group. it consists of ten chapters plus two
appendixes. the first chapter is an overview of the second to the
eighth ones. mainly， we study several different inequalities or
different types of convergence by using three mathematical tools: a
probabilistic tool， the coupling methods （chapters 2 and 3）; a
generalized cheeger’s method originating in riemannian geometry
（chapter 4）; and an approach coming from potential theory and
harmonic analysis （chapters 6 and 7）. the explicit criteria for
different types of convergence and the explicit estimates of the
convergence rates （or the optimal constants in the inequalities） in
dimension one are given in chapters 5 and 6; some generalizations
are given in chapter 7. the proofs of a diagram of nine types of
ergodicity （theorem 1.9） are presented in chapter 8.
作者简介
陈木法是中科院院士，国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
本书特色
陈木法编著的《特征值、不等式和遍历理论》详细讲述了应用广泛众多读者感兴趣的问题———矩阵的谱隙和微分算子，提供了描述相变换和随机算术效应的工具。每章以综述开始，为了吸引更多的非专业人士，通过简单例子引入观点而不是技巧证明。后面的一些章节很自然地将读者引入这个领域的问题和应用中，如经济的随机模型等。
读者对象：数学、统计、经济领域的学生和相关的科研人员。
目录
acknowledgments
chapter 1 an overview of the book
1.1 introduction
1.2 new variational formula for the first eigenvalue
1.3 basic inequalities and new forms of cheeger’s constants
1.4 a new picture of ergodic theory and explicit criteria
chapter 2 optimal markovian couplings
2.1 couplings and markovian couplings
2.2 optimality with respect to distances
2.3 optimality with respect to closed functions
2.4 applications of coupling methods
chapter 3 new variational formulas for the first
eigenvalue
3.1 background
3.2 partial proof in the discrete case
