OPTIMAL CORRECTOR ESTIMATES ON PERCOLATION CLUSTERS
Résumé
We prove optimal quantitative estimates on the first-order correctors on supercritical percolation clusters: we show that they are bounded in d ≥ 3 and have logarithmic growth in d = 2, in the sense of stretched exponential moments. The main ingredients are a renormalization scheme of the supercritical percolation cluster, following the works of Pisztora [29] and Barlow [10]; large-scale regularity estimates developed in the previous paper [7]; and a nonlinear concentration inequality of Efron-Stein type which is used to transfer quantitative information from the environment to the correctors.
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