Preface -- An Overview of the Book -- Optimal Markovian Couplings -- New Variational Formulas for the First Eigenvalue -- Generalized Cheeger's Method -- Ten Explicit Criteria in Dimension One -- Poincaré-type Inequalities in Dimension One -- Functional Inequalities -- A Diagram of Nine Types of Ergodicity -- Reaction-Diffusion Processes -- Stochastic Models of Economic Optimization -- Appendix A: Some Elementary Lemmas -- Appendix B: Examples of Ising Model on Two-Four Sites -- References -- Author Index -- Subject Index
Summary
"Eigenvalues, Inequalities, and Ergodic Theory serves as an introduction to this developing field and provides an overview of the methods used in an accessible and concise manner. The author starts with an overview chapter from which any of the following self contained chapters can be read." "Intended for researchers, graduates, and postgraduates in probability theory, Markov processes, mathematical physics, and spectrum theory, this book will be a welcome introduction to a growing area of research."--Jacket
Bibliography
Includes bibliographical references (pages 209-222)-and indexes