PR ] 3 0 M ar 2 00 4 Approximation of the effective conductivity of ergodic media by periodization .

@inproceedings{Owhadi2003PR3,
title={PR ] 3 0 M ar 2 00 4 Approximation of the effective conductivity of ergodic media by periodization .},
author={Houman Owhadi},
year={2003}
}

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 ≥ 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(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 lim N→+∞ σ(A, η) = σ(A,μ) We extend this result to non-symmetric operators ∇x(a +E(x, η))∇x corresponding… CONTINUE READING