Bovier / den Hollander


A Potential-Theoretic Approach
Softcover reprint of the original 1st ed. 2015 2018. Buch. xxi, 581 S.: 82 s/w-Abbildungen, 14 Farbabbildungen, Bibliographien. Softcover
Springer ISBN 978-3-319-79676-5
Format (B x L): 15,5 x 23,5 cm
Gewicht: 914 g
In englischer Sprache
Das Werk ist Teil der Reihe:
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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Presents a concise and authoritative potential-theoretic approach on metastability Reduces questions of interest to the computation of capacities, that in turn can be estimated by exploiting powerful variational principles Deduces detailed information on the spectral characteristics of the generator of the dynamics Unveils the common universal features of metastable systems through numerous examples