Metastability: A Potential-theoretic Approach (grundlehren Der Mathematischen Wissenschaften)
by Anton Bovier /
2016 / English / PDF
5.9 MB Download
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.
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 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 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.
The monograph will serve both as comprehensive introduction and
as reference for graduate students and researchers interested in
metastability.
