This 600-page monograph provides a concise presentation of a mathematical approach to
metastability based on potential theory of reversible Markov processes. Metastability is 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.
The monograph sheds 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.
These examples unveil the common universal features of metastable behaviour.
Anton Bovier held the Kloosterman Chair 2012 at the Mathematical Institute.