On decoupling inequalities and percolation of excursion sets of the Gaussian free field

Serguei Popov, Balazs Rath

Published 2013-07-10, updated 2015-02-04Version 3

We prove decoupling inequalities for the Gaussian free field on $\mathbb{Z}^d$, $d\geq 3$. As an application, we obtain exponential decay (with logarithmic correction for $d=3$) of the connectivity function of excursion sets for large values of the threshold.