OPTIMAL CORRECTOR ESTIMATES ON PERCOLATION CLUSTERS

Paul Dario (1, 2)

1 Université Paris Dauphine-PSL
2 DMA - Département de Mathématiques et Applications - ENS Paris

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.

Domaines: Mathématiques [math]; Probabilités [math.PR]

Paul Dario. OPTIMAL CORRECTOR ESTIMATES ON PERCOLATION CLUSTERS. 2018. ⟨hal-01818437⟩