Authors:
- First and only book to make this research available in the west
- Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist
- Each chapter is self-contained to make the book easy-to-use
- Includes supplementary material: sn.pub/extras
Part of the book series: Probability and Its Applications (PIA)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
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)
Authors and Affiliations
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Department of Mathematics, Beijing Normal University, Beijing, The People’s Republic of China
Mu-Fa Chen
About the author
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.
Bibliographic Information
Book Title: Eigenvalues, Inequalities, and Ergodic Theory
Authors: Mu-Fa Chen
Series Title: Probability and Its Applications
DOI: https://doi.org/10.1007/b138904
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2005
Hardcover ISBN: 978-1-85233-868-8Published: 10 January 2005
Softcover ISBN: 978-1-84996-938-3Published: 21 October 2010
eBook ISBN: 978-1-84628-123-5Published: 30 March 2006
Series ISSN: 1431-7028
Edition Number: 1
Number of Pages: XIII, 228