Analysis and Stochastics of Growth Processes and Interface Models

Hardcover | July 24, 2008

EditorPeter Morters, Roger Moser, Mathew Penrose

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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 beingaccessible 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 arediscussed 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 earlyuniverse. 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.

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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 beingaccessible for researchers in probability, and vice ...

Peter Morters is a professor of probability at the University of Bath. Receiving his PhD from the University of London in the area of geometric measure theory, his current interests focus on Bronwnian motion and random walk, stohastic processes in random environments, large deviation theory and, more recently random networks. Roger Mo...

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Format:HardcoverDimensions:304 pages, 9.21 × 6.14 × 0.91 inPublished:July 24, 2008Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199239258

ISBN - 13:9780199239252

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Table of Contents

PrefaceIntroductionI QUANTUM AND LATTICE MODELSQuantum and Lattice Models1.1. T. Seppalainen: Directed Random Growth Models on the Plane1.2. M. Deijfen and O. Haggstrom: The Pleasures and Pains of Studying the Two-Type Richardson Model1.3. D. Ioffe and Y. Velenik: Ballistic Phase of Self-Interacting Random WalksMicroscopic to Macroscopic Transition2.1. X. Blanc: Stochastic Homogenization and Energy of Infinite Sets of Points2.2. K. Matthies and F. Theil: Validity and Non-Validity of Propagation of ChaosApplications in Physics3.1. A. Sakai: Applications of the Lace Expansion to Statistical-Mechanical Models3.2. S. Adams: Large Deviations for Empirical Cycle Counts of Integer Partitions and Their Relation to Systems of Bosons3.3. S. Adams and W. Konig: Interacting Brownian Motions and the Gross-Pitaevskii Formula3.4. D. Hundertmark: A Short Introduction to Anderson LocalizationII MACROSCOPIC MODELSNucleation and Growth4.1. B. Niethammer: Effective Theories for Ostwald Ripening4.2. N. Dirr: Switching Paths for Ising Models with Long-Range Interaction4.3. O. Penrose: Nucleation and Droplet Growth as a Stochastic ProcessApplications in Physics5.1. A. Neate and A. Truman: On the Stochastic Burgers Equation with some Applications to Turbulence and Astrophysics5.2. A. Majumdar, J. Robbins, and M. Zyskin: Liquid Crystals and Harmonic Maps in Polyhedral DomainsIndex