This monograph provides a concise presentation of a mathematical
approach to metastability, a wide-spread phenomenon in the dynamics of
non-linear systems - physical, chemical, biological or economic -
subject to the action of temporal random forces typically referred to as
noise, based on potential theory of reversible Markov processes.
The authors shed new light on the metastability phenomenon as a sequence
of visits of the path of the process to different metastable sets, and
focuses on the precise analysis of the respective hitting probabilities
and hitting times of these sets.
The theory is illustrated with many examples, ranging from finite-state
Markov chains, finite-dimensional diffusions and stochastic partial
differential equations, via mean-field dynamics with and without
disorder, to stochastic spin-flip and particle-hop dynamics and
probabilistic cellular automata, unveiling the common universal features
of these systems with respect to their metastable behaviour.
The monograph will serve both as comprehensive introduction and as
reference for graduate students and researchers interested in
metastability.