Large Deviations and Metastability (Encyclopedia of Mathematics and its Applications)
Cambridge University Press, 2/21/2005
EAN 9780521591638, ISBN10: 0521591635
Hardcover, 528 pages, 22.8 x 15.2 x 3.4 cm
Language: English
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.