Cover image for Analysis and stochastics of growth processes and interface models
Title:
Analysis and stochastics of growth processes and interface models
Publication Information:
New York, NY : OUP Oxford, 2008
Physical Description:
x, 336 p. : ill. ; 24 cm.
ISBN:
9780199239252
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30000010226175 QA274.75 A53 2008 Open Access Book Book
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Summary

Summary

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.


Author Notes

Peter Mörters 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 Eidgenössische 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 Geometric Graphs" was published by Oxford University Press in 2003. He obtained his PhD in stohastic analysis from the University of Edinburgh.Hartmut Schwetlick is a lecturer of mathematics at the University of Bath. After receiving his PhD from the University of Tubingen in the field of nonlinear transport equations, he worked on partial differential equations and their applications at ETH Zurich and the Max Planck Institute for Mathematics in teh Sciences, Leipzig. His research interests include analysis of PDE, variational methods in geometric analysis, and nonlinear elasticity.Johannes Zimmer is currently a lecturer of applied mathematics at the University of Bath.Prior to that, he was head of an Emmy Noether group at the Max Planck Institute for Mathematics in the Sciences, Leipzig. He obtained his doctorate from the Technische universitat Munchen. Research interests include the analysis of lattice dynamical systems, and PDEs, continuum mechanics, and phase transitions.


Table of Contents

Timo SeppäläinenMaria Deijfen and Olle HäggströmDmitry Ioffe and Yuan VelenikXavier BlancKarsten Matthies and Florian TheilAkira SakaiStefan AdamsStefan Adams and Wolfgang KönigDirk HundertmarkBarbara NiethammerNicolas DirrOliver PenroseA. D. Neate and A. TrumanApala Majumdar and Jonathan Robbins and Maxim Zyskin
List of Contributorsp. ix
Introductionp. 1
Part I Quantum And Lattice Models
A Quantum and Lattice Modelsp. 7
1 Directed random growth models on the planep. 9
2 The pleasures and pains of studying the two-type Richardson modelp. 39
3 Ballistic phase of self-interacting random walksp. 55
B Microscopic to Macroscopic Transitionp. 81
4 Stochastic homogenization and energy of infinite sets of pointsp. 83
5 Validity and non-validity of propagation of chaosp. 101
C Applications in Physicsp. 121
6 Applications of the lace expansion to statistical-mechanical modelsp. 123
7 Large deviations for empirical cycle counts of integer partitions and their relation to systems of Bosonsp. 148
8 Interacting Brownian motions and the Gross-Pitaevskii formulap. 173
9 A short introduction to Anderson localizationp. 194
Part II Microscopic Models
A Nucleation and Growthp. 221
10 Effective theories for Ostwald ripeningp. 223
11 Switching paths for Ising models with long-range interactionp. 244
12 Nucleation and droplet growth as a stochastic processp. 265
B Applications in Physicsp. 279
13 On the stochastic Burgers equation with some applications to turbulence and astrophysicsp. 281
14 Liquid crystals and harmonic maps in polyhedral domainsp. 306
Indexp. 327