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Grundlehren der mathematischen Wissenschaften

Metastability

A Potential-Theoretic Approach

Authors: Bovier, Anton, den Hollander, Frank

  • 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
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eBook $54.99
$109.00 (listprice)
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  • ISBN 978-3-319-24777-9
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Hardcover $69.99
$149.00 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-3-319-24775-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

Anton Bovier is Professor of Mathematics at the University of Bonn.  His research concerns applications of probability theory in physics and biology, with a focus on statistical mechanics, metastability and ageing. He has published over 130 scientific papers, and a monograph on “Statistical Mechanics of Disordered Systems”. He is a Fellow of the Institute for Mathematical Statistics. He is member of the Clusters of Excellence “Hausdorff Centre for Mathematics” and “ImmunoSensation”, both at the University of Bonn.

Frank den Hollander is Professor of Mathematics at Leiden University. His research focuses on probability theory, statistical physics, population dynamics and complex networks. He has published over 150 scientific papers, and two monographs on “Large Deviations” and “Random Polymers”. He is a member of the Royal Dutch Academy of Sciences, and a Fellow of the American Mathematical Society and of the Institute of Mathematical Statistics. He is recipient of a 5-year Advanced Grant by the European Research Council and a 10-year consortium grant by the Dutch Ministry of Education, Culture and Science.

Reviews

“No doubt, this is a fundamental book written by well established scientists whose contribution to this area is widely recognized. The book is addressed to readers with serious mathematical background and interests in metastability of stochastic dynamical systems. The books is also an excellent references source.” (Jordan M. Stoyanov, zbMATH 1339.60002, 2016)


Table of contents (23 chapters)

  • Background and Motivation

    Bovier, Anton (et al.)

    Pages 3-13

  • Aims and Scopes

    Bovier, Anton (et al.)

    Pages 15-23

  • Some Basic Notions from Probability Theory

    Bovier, Anton (et al.)

    Pages 27-61

  • Markov Processes in Discrete Time

    Bovier, Anton (et al.)

    Pages 63-78

  • Markov Processes in Continuous Time

    Bovier, Anton (et al.)

    Pages 79-123

Buy this book

eBook $54.99
$109.00 (listprice)
price for USA (gross)
valid through June 30, 2017
  • ISBN 978-3-319-24777-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
$149.00 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-3-319-24775-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Metastability
Book Subtitle
A Potential-Theoretic Approach
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
351
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-24777-9
DOI
10.1007/978-3-319-24777-9
Hardcover ISBN
978-3-319-24775-5
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XXI, 581
Number of Illustrations and Tables
14 b/w illustrations, 82 illustrations in colour
Topics