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.

Table of Contents

• Contents of the book :
• Preface
• Introduction
• I QUANTUM AND LATTICE MODELS
• Quantum and Lattice Models
• 1.1. Directed Random Growth Models on the Plane , T. Seppäläinen
• 1.2. The Pleasures and Pains of Studying the Two-Type Richardson Model , M. Deijfen and O. Häggström
• 1.3. Ballistic Phase of Self-Interacting Random Walks , D. Ioffe and Y. Velenik
• Microscopic to Macroscopic Transition
• 2.1. Stochastic Homogenization and Energy of Infinite Sets of Points , X. Blanc
• 2.2. Validity and Non-Validity of Propagation of Chaos , K. Matthies and F. Theil
• Applications in Physics
• 3.1. Applications of the Lace Expansion to Statistical-Mechanical Models , A. Sakai
• 3.2. Large Deviations for Empirical Cycle Counts of Integer Partitions and Their Relation to Systems of Bosons , S. Adams
• 3.3. Interacting Brownian Motions and the Gross-Pitaevskii Formula , S. Adams and W. König
• 3.4. A Short Introduction to Anderson Localization , D. Hundertmark
• II MACROSCOPIC MODELS
• Nucleation and Growth
• 4.1. Effective Theories for Ostwald Ripening , B. Niethammer
• 4.2. Switching Paths for Ising Models with Long-Range Interaction , N. Dirr
• 4.3. Nucleation and Droplet Growth as a Stochastic Process , O. Penrose
• Applications in Physics
• 5.1. On the Stochastic Burgers Equation with some Applications to Turbulence and Astrophysics ,
• A. Neate and A. Truman
• 5.2. Liquid Crystals and Harmonic Maps in Polyhedral Domains , A. Majumdar, J. Robbins, and M. Zyskin