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Author Owhadi, Houman
Source SpringerLink
Content type Text
Publisher Springer-Verlag
File Format PDF
Copyright Year ©2003
Language English
Subject Domain (in DDC) Social sciences ♦ Sociology & anthropology
Abstract  This paper is concerned with the approximation of the effective conductivity σ(A, μ) associated to an elliptic operator ∇ xA (x,η)∇ x where for xℝ d , d≥1, A(x,η) is a bounded elliptic random symmetric d×d matrix and η takes value in an ergodic probability space (X, μ). Writing A N (x, η) the periodization of A(x, η) on the torus T d N of dimension d and side N we prove that for μ-almost all η We extend this result to non-symmetric operators ∇ x (a+E(x, η))∇ x corresponding to diffusions in ergodic divergence free flows (a is d×d elliptic symmetric matrix and E(x, η) an ergodic skew-symmetric matrix); and to discrete operators corresponding to random walks on ℤ d with ergodic jump rates. The core of our result is to show that the ergodic Weyl decomposition associated to 2(X, μ) can almost surely be approximated by periodic Weyl decompositions with increasing periods, implying that semi-continuous variational formulae associated to 2(X, μ) can almost surely be approximated by variational formulae minimizing on periodic potential and solenoidal functions.
ISSN 01788051
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2003-02-01
Publisher Place Berlin Heidelberg
e-ISSN 14322064
Journal Probability Theory and Related Fields
Volume Number 125
Issue Number 2
Page Count 34
Starting Page 225
Ending Page 258

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Source: SpringerLink