# 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} }

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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