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Metastability - A Potential-Theoretic Approach (Hardcover, 1st ed. 2015)
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Metastability - A Potential-Theoretic Approach (Hardcover, 1st ed. 2015)
Series: Grundlehren der mathematischen Wissenschaften, 351
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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.
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