Eigenvalues, Inequalities and Ergodic Theory

Mu-Fa Chen - Collection Probability and Its Applications

228 pages, parution le 11/02/2005

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Résumé

A problem of broad interest - the estimation of the spectral gap for matrices or differential operators (Markov chains or diffusions) - is covered in this book. In particular, it studies a subset of the general problem, taking some approaches that have, up till now, only appeared largely in the Chinese literature.

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.

Each chapter starts with a summary and, in order to appeal to non-specialists, ideas are introduced through simple examples rather than technical proofs. In the latter chapters readers are introduced to problems and application areas, including stochastic models of economy.

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.

L'auteur - Mu-Fa Chen

Mu-Fa Chen is Professor of Mathematics at Beijing Normal University in the People's Republic of China, and Member of the Chinese Academy of Sciences. In 1999 he received a Prize for Progress on Sciences and Technology from the Ministry of Education and a National Prize on Natural Sciences from the Ministry of Science and Technology in the People's Republic of China.

Sommaire

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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Mu-Fa Chen
Collection	Probability and Its Applications
Parution	11/02/2005
Nb. de pages	228
Format	16 x 24
Couverture	Relié
Poids	472g
Intérieur	Noir et Blanc
EAN13	9781852338688
ISBN13	978-1-85233-868-8