Mörters P., Moser R., Penrose M. et. al. Analysis and stochastics of growth processes and interface models

New York, Oxford University Press Inc., 2008, 336 p.A regional meeting of the London Mathematical Society, followed by a workshop on ‘Analysis and Stochastics of Growth Processes’, was held at the University of Bath on 11–15 September 2006. The aim of these events was to bring together analysts and probabilists working on the mathematical description of growth phenomena, with models based on the physics of individual particles discussed alongside models based on the continuum description of large collections of particles.
Convinced by positive feedback from the participants that this exercise in interdisciplinary exchange was worthwhile, we invited the speakers of the meeting and the workshop to contribute to this volume with an article in the same spirit. We hope that the resulting collection will help bridge the gap between researchers studying phenomena of the same type with different approaches. The meeting and the workshop were funded by the London Mathematical Society and the Bath Institute for Complex Systems, whose generous support is gratefully acknowledged.QUANTUM AND LATTICE MODELS
Quantum and Lattice Model
Directed random growth models on the plane
The pleasures and pains of studying the two-type Richardson model
Ballistic phase of self-interacting random walks
B Microscopic to Macroscopic Transition
Stochastic homogenization and energy of infinite sets of points
Validity and non-validity of propagation of chaos
C Applications in Physics
Applications of the lace expansion to statistical-mechanical models
Large deviations for empirical cycle counts of integer partitions and their relation to systems of Bosons
Interacting Brownian motions and the Gross–Pitaevskii formula
A short introduction to Anderson localization
MICROSCOPIC MODELS
A Nucleation and Growth
Effective theories for Ostwald ripening
Switching paths for Ising models with long-range interaction
Nucleation and droplet growth as a stochastic process
B Applications in Physics
On the stochastic Burgers equation with some applications to turbulence and astrophysics
Liquid crystals and harmonic maps in polyhedral domains