# Annealed estimates on the Green function

@article{Marahrens2013AnnealedEO,
title={Annealed estimates on the Green function},
author={Daniel Marahrens and Felix Otto},
journal={Probability Theory and Related Fields},
year={2013},
volume={163},
pages={527-573}
}
• Published 16 April 2013
• Mathematics
• Probability Theory and Related Fields
We consider a random, uniformly elliptic coefficient field $$a(x)$$a(x) on the $$d$$d-dimensional integer lattice $$\mathbb {Z}^d$$Zd. We are interested in the spatial decay of the quenched elliptic Green function $$G(a;x,y)$$G(a;x,y). Next to stationarity, we assume that the spatial correlation of the coefficient field decays sufficiently fast to the effect that a logarithmic Sobolev inequality holds for the ensemble $$\langle \cdot \rangle$$⟨·⟩. We prove that all stochastic moments of the…
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