The book provides a general introduction to the theory of large deviations and a wide overview of the metastable behaviour of stochastic dynamics. With only minimal prerequisites, the book covers all the main results and brings the reader to the most recent developments. Particular emphasis is given to the fundamental Freidlin-Wentzell results on small random perturbations of dynamical systems. Metastability is first described on physical grounds, following which more rigorous approaches to its description are developed. Many relevant examples are considered from the point of view of the so-called pathwise approach. The first part of the book develops the relevant tools including the theory of large deviations which are then used to provide a physically relevant dynamical description of metastability. Written to be accessible to graduate students, this book provides an excellent route into contemporary research.
• Concrete applications of large deviation theory • First treatment of metastability in book form • Self-contained and accessible to graduate students, whilst containing many recent developments
Contents
Preface; 1. Large deviations: basic results; 2. Small random perturbations of dynamical systems: basic estimates of Freidlin and Wentzell; 3. Large deviations and statistical mechanics; 4. Metastability I: general description, the Curie-Weiss model and contact processes; 5. Metastability II: the models of Freidlin and Wentzell; 6. Reversible Markov chains in the Freidlin-Wentzell regime; 7. Metastable behaviour for lattice spin models at low temperature; Bibliography; Index.
Reviews
'This impressive monograph provides a quite complete survey of the topic of metastability and will certainly be a very useful reference for all research activity in this field.' Publication of the International Statistical Institute
' … yields a wide overview of the current mathematical understanding of metastability phenomena arising in the context of Markov processes.' Zentralblatt MATH
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