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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.

Large deviations. --- Stability. --- Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Deviations, Large --- Limit theorems (Probability theory) --- Statistics --- Mathematical statistics --- Large deviations --- Stability

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Large deviations --- Mathematical statistics --- Probabilities --- Grandes déviations --- Statistique mathématique --- Probabilités

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Large deviations

Probability theory --- Large deviations. --- Limit theorems (Probability theory) --- 519.21 --- 519.22 --- Large deviations --- Deviations, Large --- Statistics --- 519.22 Statistical theory. Statistical models. Mathematical statistics in general --- Statistical theory. Statistical models. Mathematical statistics in general --- 519.21 Probability theory. Stochastic processes --- Probability theory. Stochastic processes --- Probabilities

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Ergodic theory. Information theory --- Central limit theorem --- Large deviations --- Markov processes --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Deviations, Large --- Limit theorems (Probability theory) --- Statistics --- Asymptotic distribution (Probability theory) --- Central limit theorem. --- Théorème de la limite centrale --- Markov processes. --- Markov, Processus de --- Large deviations. --- Grandes déviations --- Théorème de la limite centrale. --- Markov, Processus de. --- Grandes déviations.