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

Abstract

We prove decoupling inequalities for the Gaussian free field on ${\mathbb{Z}}^d$, $d\ge 3$. 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.

12 pages

References in corpus (1)

• From loop clusters and random interlacement to the free field

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