High order correctors in stochastic homogenization: moment bounds

Yu Gu

Published 2016-01-29Version 1

In this note, we study high order correctors in stochastic homogenization. For discrete elliptic equations in divergence form on $\mathbb{Z}^d$, when the random coefficients are constructed from i.i.d. random variables, we prove arbitrary high order moment bounds on the $n-$th order corrector when $d\geq 2n+1$. It implies the existence of stationary $n-$th order correctors under the dimension constraint. The proof is based on the recent work of \cite{gloria2011optimal,marahrens2013annealed}.