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Metastability

A Potential-Theoretic Approach

  • Anton Bovier
  • Frank den Hollander

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 351)

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Anton Bovier, Frank den Hollander
      Pages 3-13
    3. Anton Bovier, Frank den Hollander
      Pages 15-23
  3. Markov Processes

    1. Front Matter
      Pages 25-25
    2. Anton Bovier, Frank den Hollander
      Pages 27-61
    3. Anton Bovier, Frank den Hollander
      Pages 63-78
    4. Anton Bovier, Frank den Hollander
      Pages 79-123
    5. Anton Bovier, Frank den Hollander
      Pages 125-143
    6. Anton Bovier, Frank den Hollander
      Pages 145-185
  4. Metastability

    1. Front Matter
      Pages 187-187
    2. Anton Bovier, Frank den Hollander
      Pages 189-226
    3. Anton Bovier, Frank den Hollander
      Pages 227-243
  5. Applications: Diffusions with Small Noise

    1. Front Matter
      Pages 245-245
    2. Anton Bovier, Frank den Hollander
      Pages 247-263
    3. Anton Bovier, Frank den Hollander
      Pages 265-304
    4. Anton Bovier, Frank den Hollander
      Pages 305-321
  6. Applications: Coarse-Graining in Large Volumes at Positive Temperatures

    1. Front Matter
      Pages 323-323
    2. Anton Bovier, Frank den Hollander
      Pages 325-330
    3. Anton Bovier, Frank den Hollander
      Pages 331-344
    4. Anton Bovier, Frank den Hollander
      Pages 345-380
  7. Applications: Lattice Systems in Small Volumes at Low Temperatures

    1. Front Matter
      Pages 381-381
    2. Anton Bovier, Frank den Hollander
      Pages 383-408
    3. Anton Bovier, Frank den Hollander
      Pages 409-424
    4. Anton Bovier, Frank den Hollander
      Pages 425-457
  8. Applications: Lattice Systems in Large Volumes at Low Temperatures

    1. Front Matter
      Pages 459-459
    2. Anton Bovier, Frank den Hollander
      Pages 461-477
    3. Anton Bovier, Frank den Hollander
      Pages 479-507
  9. Applications: Lattice Systems in Small Volumes at High Densities

    1. Front Matter
      Pages 509-509
    2. Anton Bovier, Frank den Hollander
      Pages 511-541
  10. Challenges

    1. Front Matter
      Pages 543-543
    2. Anton Bovier, Frank den Hollander
      Pages 545-558
    3. Anton Bovier, Frank den Hollander
      Pages 559-563
  11. Back Matter
    Pages 565-581

About this book

Introduction

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.

Keywords

60K35, 60J45, 82C26 Markov processes interacting particle systems metastability phase transitions potential theory

Authors and affiliations

  • Anton Bovier
    • 1
  • Frank den Hollander
    • 2
  1. 1.Rhein. Friedrich-Wilhelms UniversitätInstitut für Angewandte MathematikBonnGermany
  2. 2.Mathematisch InstituutUniversiteit LeidenLeidenThe Netherlands

Bibliographic information

  • 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
  • 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
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