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Analysis and Stochastics of Growth Processes and Interface Models
Edited by Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, and Johannes Zimmer
352 pages
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234x156mm
978-0-19-923925-2
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Hardback
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24 July 2008
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- Highly accessible.
- Contributing authors are leading authors in the field.
- Important and topical resource for analysis and probability communities.
This book is a collection of topical survey articles by leading researchers in the fields of applied analysis and probability theory, working on the mathematical description of growth phenomena. Particular emphasis is on the interplay of the two fields, with articles by analysts being accessible for researchers in probability, and vice versa. Mathematical methods discussed in the book comprise large deviation theory, lace expansion, harmonic multi-scale techniques and homogenisation of partial differential equations. Models based on the physics of individual particles are discussed alongside models based on the continuum description of large
collections of particles, and the mathematical theories are used to describe physical phenomena such as droplet formation, Bose-Einstein condensation, Anderson localization, Ostwald ripening, or the formation of the early universe. The combination of articles from the two fields of analysis and probability is highly unusual and makes this book an important resource for researchers working in all areas close to the interface of these fields.Readership: Graduates and researchers in Probability, Analysis and Physics.
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Edited by Peter Mörters, Professor of Probability, University of Bath, Roger Moser, Lecturer in Mathematics, University of Bath, Mathew Penrose, Professor of Probability, University of Bath, Hartmut Schwetlick, Lecturer in Mathematics, University of Bath, and Johannes Zimmer, Lecturer in Applied Mathematics, University of Bath Contributors:
T. Seppäläinen
M. Deijfen and O. Häggström
D. Ioffe and Y. Velenik
X. Blanc
K. Matthies and F. Theil
A. Sakai
S. Adams
S. Adams and W. König
D.
Hundertmark
B. Niethammer
N. Dirr
O. Penrose
A. Neate and A. Truman
A. Majumdar, J. Robbins, and M. Zyskin
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Preface
Introduction
I QUANTUM AND LATTICE MODELS
Quantum and Lattice Models
1.1: T. Seppäläinen: Directed Random Growth Models on the Plane
1.2: M. Deijfen and O. Häggström: The Pleasures and Pains of Studying the Two-Type Richardson Model
1.3: D. Ioffe and Y. Velenik: Ballistic Phase of Self-Interacting Random Walks
Microscopic to Macroscopic Transition
2.1: X. Blanc: Stochastic Homogenization and Energy of Infinite Sets of Points
2.2: K. Matthies and F. Theil: Validity and Non-Validity of Propagation of Chaos
Applications in Physics
3.1: A. Sakai: Applications of the Lace Expansion to Statistical-Mechanical Models
3.2: S. Adams: Large Deviations for Empirical Cycle Counts of Integer Partitions and Their Relation to Systems of Bosons
3.3: S. Adams and W. König: Interacting Brownian Motions and the Gross-Pitaevskii Formula
3.4: D. Hundertmark: A Short Introduction to Anderson Localization
II MACROSCOPIC MODELS
Nucleation and Growth
4.1: B. Niethammer: Effective Theories for Ostwald Ripening
4.2: N. Dirr: Switching Paths for Ising Models with Long-Range Interaction
4.3: O. Penrose: Nucleation and Droplet Growth as a Stochastic Process
Applications in Physics
5.1: A. Neate and A. Truman: On the Stochastic Burgers Equation with some Applications to Turbulence and Astrophysics
5.2: A. Majumdar, J. Robbins, and M. Zyskin: Liquid Crystals and Harmonic Maps in Polyhedral Domains
Index
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