Fr. 135.00

Eigenvalues, Inequalities, and Ergodic Theory

Inglese · Copertina rigida

Spedizione di solito entro 6 a 7 settimane

Descrizione

Ulteriori informazioni

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.

Sommario

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.

Info autore

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.

Riassunto

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.

Testo aggiuntivo

From the reviews of the first edition:

"The estimation of the spectral gap for matrices or differential operators (Markov chain or diffusions) – is covered in this book, and the book surveys, in popular way, the main progress made in the field. … Each chapter starts with a summary, and ideas are introduced through simple examples rather than technical proofs, which is one of the advantages of the book … . The book may be useful for researchers, graduates and postgraduates in probability theory, Markov processes, mathematical physics and spectrum theory." (Anatoliy Swishchuk, Zentralblatt MATH, Vol. 1079, 2006)

"The main topics of this book, as indicated in the title, are eigenvalues, inequalities, and ergodic theory. … Chen is an experienced researcher who has won prizes in China and spoken at the International Congress of Math, and he is an extensive writer of lecture notes. … The math is clearly explained and the book is pleasant to read. … it deserves a place on your bookshelf." (Rick Durrett, SIAM Review, Vol. 48 (1), 2006)

Relazione

From the reviews of the first edition:

"The estimation of the spectral gap for matrices or differential operators (Markov chain or diffusions) - is covered in this book, and the book surveys, in popular way, the main progress made in the field. ... Each chapter starts with a summary, and ideas are introduced through simple examples rather than technical proofs, which is one of the advantages of the book ... . The book may be useful for researchers, graduates and postgraduates in probability theory, Markov processes, mathematical physics and spectrum theory." (Anatoliy Swishchuk, Zentralblatt MATH, Vol. 1079, 2006)
"The main topics of this book, as indicated in the title, are eigenvalues, inequalities, and ergodic theory. ... Chen is an experienced researcher who has won prizes in China and spoken at the International Congress of Math, and he is an extensive writer of lecture notes. ... The math is clearly explained and the book is pleasant to read. ... it deserves a place on your bookshelf." (Rick Durrett, SIAM Review, Vol. 48 (1), 2006)

Dettagli sul prodotto

Autori Mu-Fa Chen
Editore Springer, Berlin
 
Lingue Inglese
Formato Copertina rigida
Pubblicazione 17.01.2005
 
EAN 9781852338688
ISBN 978-1-85233-868-8
Pagine 228
Dimensioni 165 mm x 239 mm x 21 mm
Peso 545 g
Illustrazioni XIII, 228 p.
Serie Probability and Its Applications
Probability and Its Applicatio
Probability and its Applications
Probability and Its Applicatio
Categorie Scienze naturali, medicina, informatica, tecnica > Matematica > Teoria delle probabilità, stocastica, statistica matematica

B, Mathematics and Statistics, Probability Theory and Stochastic Processes, Probabilities, Stochastics, Probability Theory

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