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Analysis and Stochastics of Growth Processes and Interface Models$
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Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, and Johannes Zimmer

Print publication date: 2008

Print ISBN-13: 9780199239252

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199239252.001.0001

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Directed Random Growth Models on the Plane

Directed Random Growth Models on the Plane

Chapter:
(p.9) 1 Directed Random Growth Models on the Plane
Source:
Analysis and Stochastics of Growth Processes and Interface Models
Author(s):

Timo Seppäläinen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199239252.003.0001

This chapter discusses random growth models describing the evolution of an interface in the plane. For specific models, three basic questions are discussed. First, under appropriate scaling, what is the limiting shape of the interface and what is the partial differential equation governing its evolution? Second, how can random fluctuations around the limit behaviour be described? Third, how can atypical behaviour be characterized? The power of probabilistic tools is demonstrated by employing laws of large numbers, central limit theorems, and large deviation techniques to answer these questions, respectively.

Keywords:   interface models, growth, continuum limit, random fluctuations, large deviation techniques

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