Large deviations and metastability /
Large Deviations & Metastability
Enzo Olivieri, Maria Eulália Vares.
- Cambridge : Cambridge University Press, 2005.
- 1 online resource (xv, 512 pages) : digital, PDF file(s).
- Encyclopedia of mathematics and its applications ; volume 100 .
- Encyclopedia of mathematics and its applications ; v. 100. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Large deviations : basic results -- Small random perturbations of dynamical systems : basic estimates of Freidlin and Wentzell -- Large deviations and statistical mechanics -- Metastability : general description : Curie-Weiss model : contact process -- Metastability : models of Freidlin and Wentzell -- Reversible Markov chains in the Freidlin-Wentzell regime -- Metastable behaviour for lattice spin models at low temperature. 1. 2. 3. 4. 5. 6. 7.
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.