Metastability : A Potential-Theoretic Approach / by Anton Bovier, Frank den Hollander.

Format:

Book

Author/Creator:

Bovier, Anton., Author.

den Hollander, Frank., Author.

Series:

Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 2196-9701 ; 351

Language:

English

Subjects (All):

Probabilities.

Mathematical physics.

Probability Theory.

Mathematical Physics.

Theoretical, Mathematical and Computational Physics.

Local Subjects:

Probability Theory.

Mathematical Physics.

Theoretical, Mathematical and Computational Physics.

Physical Description:

1 online resource (578 p.)

Edition:

1st ed. 2015.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

Language Note:

English

Summary:

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.

Contents:

Part I Introduction

1.Background and motivation

2.Aims and scopes

Part II Markov processes 3.Some basic notions from probability theory

4.Markov processes in discrete time

5.Markov processes in continuous time

6.Large deviations

7.Potential theory

Part III Metastability

8.Key definitions and basic properties

9.Basic techniques

Part IV Applications: Diffusions with small noise

10.Discrete reversible diffusions

11.Diffusion processes with gradient drift

12.Stochastic partial differential equations

Part V Applications: Coarse-graining at positive temperatures

13.The Curie-Weiss model

14.The Curie-Weiss model with a random magnetic field: discrete distributions

15.The Curie-Weiss model with random magnetic field: continuous distributions

Part VI Applications: Lattice systems in small volumes at low temperatures

16.Abstract set-up and metastability in the zero-temperature limit

17.Glauber dynamics

18.Kawasaki dynamics

Part VII Applications: Lattice systems in large volumes at low temperatures

19.Glauber dynamics

20.Kawasaki dynamics

Part VIII Applications: Lattice systems in small volumes at high densities

21.The zero-range process

Part IX Challenges

22.Challenges within metastability

23.Challenges beyond metastability

References.-Glossary

Index. .

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

3-319-24777-8