Analysis and Stochastics of Growth Processes and Interface Models

ISBN: 9780199239252 出版年：2008 页码：347 Oxford University Press

PREFACE INTRODUCTION I QUANTUM AND LATTICE MODELS QUANTUM AND LATTICE MODELS 1.1 Directed Random Growth Models on the Plane 1.2 The Pleasures and Pains of Studying the Two-Type Richardson Model 1.3 Ballistic Phase of Self-Interacting Random Walks MICROSCOPIC TO MACROSCOPIC TRANSITION 2.1 Stochastic Homogenization and Energy of Infinite Sets of Points 2.2 Validity and Non-Validity of Propagation of Chaos APPLICATIONS IN PHYSICS 3.1 Applications of the Lace Expansion to Statistical-Mechanical Models 3.2 Large Deviations for Empirical Cycle Counts of Integer Partitions and Their Relation to Systems of Bosons 3.3 Interacting Brownian Motions and the Gross-Pitaevskii Formula 3.4 A Short Introduction to Anderson Localization II MACROSCOPIC MODELS NUCLEATION AND GROWTH 4.1 Effective Theories for Ostwald Ripening 4.2 Switching Paths for Ising Models with Long-Range Interaction 4.3 Nucleation and Droplet Growth as a Stochastic Process APPLICATIONS IN PHYSICS 5.1 On the Stochastic Burgers Equation with some Applications to Turbulence and Astrophysics 5.2 Liquid Crystals and Harmonic Maps in Polyhedral Domains INDEX