Eigenvalues, Inequalities, and Ergodic Theory
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Beschreibung
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. The area has a wide range of applications, and provides a tool to describe the phase transitions and the effectiveness of random algorithms. In particular, the book 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. The author starts with an overview chapter, from which any of the following self-contained chapters can be read.
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.
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.
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
Autor*in
Mu-Fa Chen
Themen in »Eigenvalues, Inequalities, and Ergodic Theory«
Ergodic theory Markov chain Markov chains Markov process Markov processes Probability theory algorithms diffusion process ergodicity ergodig theory linear optimization mathematical physics optimization spectrum theory
Stimmen zu »Eigenvalues, Inequalities, and Ergodic Theory«
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)
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