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.