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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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Stochastic Homogenization and Energy of Infinite Sets of Points

Stochastic Homogenization and Energy of Infinite Sets of Points

Chapter:
(p.83) 4 Stochastic Homogenization and Energy of Infinite Sets of Points
Source:
Analysis and Stochastics of Growth Processes and Interface Models
Author(s):

Xavier Blanc

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199239252.003.0004

This chapter presents, in a synthetic way, a series of recent works by X. Blanc, C. Le Bris, and P-L. Lions on homogenization of an elliptic partial differential equation under certain periodic or random assumptions. The coefficients are non-constant but are a stationary random deformation of a periodic set of coefficients; a limit is taken where the period (in d-space) of the periodicity shrinks to zero. The chapter also describes related work on average energies of nonperiodic infinite sets of points.

Keywords:   stochastic homogenization, thermodynamic limit, elliptic partial differential equation

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