# Equality of critical parameters for percolation of Gaussian free field level-sets

@article{DuminilCopin2020EqualityOC, title={Equality of critical parameters for percolation of Gaussian free field level-sets}, author={Hugo Duminil-Copin and Subhajit Goswami and Pierre-François Rodriguez and Franco Severo}, journal={arXiv: Probability}, year={2020} }

We consider level-sets of the Gaussian free field on $\mathbb Z^d$, for $d\geq 3$, above a given real-valued height parameter $h$. As $h$ varies, this defines a canonical percolation model with strong, algebraically decaying correlations. We prove that three natural critical parameters associated to this model, namely $h_{**}(d)$, $h_{*}(d)$ and $\bar h(d)$, respectively describing a well-ordered subcritical phase, the emergence of an infinite cluster, and the onset of a local uniqueness regime…

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