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特征值，不等式和遍历理论PDF|Epub|txt|kindle电子书版本网盘下载
- 陈木法著 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：9787510052675
- 出版时间：2013
- 标注页数：228页
- 文件大小：32MB
- 文件页数：242页
- 主题词：特征值－不等式－英文；遍历性理论－英文
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图书目录
Chapter 1 An Overview of the Book1
1.1 Introduction1
1.2 New variational formula for the first eigenvalue3
1.3 Basic inequalities and new forms of Cheeger's constants10
1.4 A new picture of ergodic theory and explicit criteria12
Chapter 2 Optimal Markovian Couplings17
2.1 Couplings and Markovian couplings17
2.2 Optimality with respect to distances26
2.3 Optimality with respect to closed functions31
2.4 Applications of coupling methods33
Chapter 3 New Variational Formulas for the First Eigenvalue41
3.1 Background41
3.2 Partial proof in the discrete case43
3.3 The three steps of the proof in the geometric case47
3.4 Two difficulties50
3.5 The final step of the proof of the formula54
3.6 Comments on different methods56
3.7 Proof in the discrete case（continued）58
3.8 The first Dirichlet eigenvalue62
Chapter 4 Generalized Cheeger's Method67
4.1 Cheeger's method67
4.2 A generalization68
4.3 New results70
4.4 Splitting technique and existence criterion71
4.5 Proof of Theorem 4.4 77
4.6 Logarithmic Sobolev inequality80
4.7 Upper bounds83
4.8 Nash inequality85
4.9 Birth-death processes87
Chapter 5 Ten Explicit Criteria in Dimension One89
5.1 Three traditional types of ergodicity89
5.2 The first（nontrivial）eigenvalue（spectral gap）92
5.3 The first eigenvalues and exponentially ergodic rate95
5.4 Explicit criteria98
5.5 Exponential ergodicity for single birth processes100
5.6 Strong ergodicity106
Chapter 6 Poincaré-Type Inequalities in Dimension One113
6.1 Introduction113
6.2 Ordinary Poincaré inequalities115
6.3 Extension:normed linear spaces119
6.4 Neumann case:Orlicz spaces121
6.5 Nash inequality and Sobolev-type inequality123
6.6 Logarithmic Sobolev inequality125
6.7 Partial proofs of Theorem 6.1 127
Chapter 7 Functional Inequalities131
7.1 Statement of results131
7.2 Sketch of the proofs137
7.3 Comparison with Cheeger's method140
7.4 General convergenee speed142
7.5 Two functional inequalities143
7.6 Algebraic convergenee145
7.7 General（irreversible）case147
Chapter 8 A Diagram of Nine Types of Ergodicity149
8.1 Statements of results149
8.2 Applications and comments152
8.3 Proof of Theorem 1.9 155
Chapter 9 Reaction-Diffusion Processes163
9.1 The models164
9.2 Finite-dimensional case166
9.3 Construction of the processes170
9.4 Ergodicity and phase transitions175
9.5 Hydrodynamic limits177
Chapter 10 Stochastic Models of Economic Optimization181
10.1 Input-output method181
10.2 L.K.Hua's fundamental theorem182
10.3 Stochastic model without consumption186
10.4 Stochastic model with consumption188
10.5 Proof of Theorem 10.4 190
Appendix A Some Elementary Lemmas193
Appendix B Examples of the Ising Model on Two to Four Sites197
B.1 The model197
B.2 Distance based on symmetry:two sites198
B.3 Reduction:three sites200
B.4 Modification:four sites205
References209
Author Index223
Subject Index226