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arXiv · 1805.00902

Optimal corrector estimates on percolation clusters

Paul Dario
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Abstract

We prove optimal quantitative estimates on the first-order correctors on supercritical percolation clusters: we show that they are bounded in $d\geq 3$ 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 and Barlow; large-scale regularity estimates developed in the previous paper; 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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Paul Dario. 2018-05-02. Optimal corrector estimates on percolation clusters. https://arxiv.org/abs/1805.00902

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