Table of contents
Applications: Diffusions with Small Noise
Applications: Coarse-Graining in Large Volumes at Positive Temperatures
Applications: Lattice Systems in Small Volumes at Low Temperatures
Applications: Lattice Systems in Large Volumes at Low Temperatures
Applications: Lattice Systems in Small Volumes at High Densities
About this book
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. This monograph provides a concise presentation of mathematical approach to metastability 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 focus 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-hopping 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.
- DOI https://doi.org/10.1007/978-3-319-24777-9
- Copyright Information Springer International Publishing Switzerland 2015
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-3-319-24775-5
- Online ISBN 978-3-319-24777-9
- Series Print ISSN 0072-7830
- Series Online ISSN 2196-9701
- Buy this book on publisher's site