特征值.不等式和遍历理论-(影印版)

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作者：陈木法

出版社：世界图书出版公司

本类榜单：自然科学

分类：自然科学 > 数学 > 代数数论组合理论

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ISBN：9787510052675
装帧：一般胶版纸
册数：暂无
重量：暂无
开本：24开
页数：228
出版时间：2013-01-01
条形码：9787510052675 ; 978-7-5100-5267-5

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。

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.

preface
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

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