Large Deviations and Metastability

Covers an area at intersection of probability theory and statistical mechanics.

Enzo Olivieri (Author), Maria Eulália Vares (Author)

9780521591638, Cambridge University Press

Hardback, published 21 February 2005

528 pages, 37 b/w illus.
24.1 x 16.4 x 3.4 cm, 0.917 kg

' … yields a wide overview of the current mathematical understanding of metastability phenomena arising in the context of Markov processes.' Zentralblatt MATH

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.

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.

Subject Areas: Nonlinear science [PBWR], Stochastics [PBWL]