Analysis and Stochastics of Groth Processes and Interface Models [Hardcover]

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.

Peter M?rters 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 Moser is a lecturer of mathematics at the University of Bath. He received his PhD from the Eidgen?ssische Technische Hochschule Zurich in the area of geometric analysis. Further current research interests include the theory of partial differential equations, the calculus of variations, geometric measure theory, and applications if mathematical phsyics.

Mathew Penrose is a professor of Probability at the University of Bath. His current research interests are mainly in stohastic geometry and interacting particle systems. His monograph Random Geometrl$