- 特征值不等式和遍历理论
- - 作者：陈木法
  - 出版社：世界图书出版公司
  - ISBN：9787510052675
  - 出版日期：2013/01/01
  - 页数：228
- 售价：18

内容大纲
作者介绍
目录
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
  3.3  The three steps of the proof in the geometric case
  3,4  Two difficulties
  3.5  The final step of the proof of the formula
  3.6  Comments on different methods
  3.7  Proof in the discrete case (continued)
  3.8  The first Dirichlet eigenvalue
Chapter 4  Generalized Cheeger's Method
  4.1  Cheeger's method
  4.2  A generalization
  4.3  New results
  4.4  Splitting technique and existence criterion
  4.5  Proof of Theorem 4.4
  4.6  Logarithmic Sobolev inequality
  4.7  Upper bounds
  4.8  Nash inequality
  4.9  Birth-death processes
Chapter 5  Ten Explicit Criteria in Dimension One
  5.1  Three traditional types of ergodicity
  5.2  The first (nontrivial) eigenvalue (spectral gap)
  5.3  The first eigenvalues and exponentially ergodic rate
  5.4  Explicit criteria
  5.5  Exponential ergodicity for single birth processes
  5.6  Strong ergodicity
Chapter 6  Poincar-Type Inequalities in Dimension One
  6.1  Introduction
  6.2  Ordinary Poincar inequalities
  6.3  Extension: normed linear spaces
  6.4  Neumann case: Orlicz spaces
  6.5  Nash inequality and Sobolev-type inequality
  6.6  Logarithmic Sobolev inequality
  6.7  Partial proofs of Theorem 6.1
Chapter 7  Functional Inequalities
  7.1  Statement of results
  7.2  Sketch of the proofs
  7.3  Comparison with Cheeger's method

  7.4  General convergence speed
  7.5  Two functional inequalities
  7.6  Algebraic convergence
  7.7  General (irreversible) case
Chapter 8  A Diagram of Nine Types of Ergodicity
  8.1  Statements of results
  8.2  Applications and comments
  8.3  Proof of Theorem 1.9
Chapter 9  Reactlon-Diffusion Processes
  9.1  The models
  9.2  Finite-dimensional case
  9.3  Construction of the processes
  9.4  Ergodicity and phase transitions
  9.5  Hydrodynamic limits
Chapter 10  Stochastic Models of Economic Optimization
  10.1 Input-output method
  10.2 L.K. Hua's fundamental theorem
  10.3 Stochastic model without consumption
  10.4 Stochastic model with consumption
  10.5 Proof of Theorem 10.4
Appendix A  Some Elementary Lemmas
Appendix B  Examples of the Ising Model on Two to Four Sites
  B.1  The model
  B.2 Distance based on symmetry: two sites
  B.3 Reduction: three sites
  B.4 Modification: four sites
References
Author Index
Subject Index

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