# Eigenvalues, Inequalities, and Ergodic Theory

Part of the Probability and Its Applications book series (PIA)

Part of the Probability and Its Applications book series (PIA)

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.

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

- DOI https://doi.org/10.1007/b138904
- Copyright Information Springer-Verlag London Limited 2005
- Publisher Name Springer, London
- eBook Packages Mathematics and Statistics
- Print ISBN 978-1-85233-868-8
- Online ISBN 978-1-84628-123-5
- Series Print ISSN 1431-7028
- About this book